EAS 508 Assignment 1– Lolla Aditya Srivatsav and 50559685 here
library(ISLR2)
library(ggplot2)In case you need to write math expression, please use the quick tutorial as the reference: https://www1.cmc.edu/pages/faculty/aaksoy/latex/latexthree.html
Question 1
[5 pts] Describe a situation or problem from your job, everyday life, current events, etc., for which a classification model would be appropriate. List some (up to 5) predictors that you might use.
Solution to Question 1 There are many events which we can use in everyday life to classify the models or events in the market 1. Credit Score: A high Credit will have a secured loan where there will be low risk 2. Job Status and Secured House: A job with fixed income can pay their debts for the long time and any business can be filed in the UCC1 and UCC3 and approved from the jurisdiction 3.Aerospace Manufacturing: An Aerospace or Air Force plane manufacturing companies can plot the details for the new flights and get the raw data requirements, budget can be classified with the classification models and prepare the data for the further process. 4. Debt-to-Income Ratio: A lower ratio suggests that the applicant has manageable debt relative to their income. 5.Loan Amount: Larger loan amounts might increase the risk of default, especially if they exceed the applicant’s capacity to repay.
Question 2.
[5 pts] What’s the main difference between supervised and unsupervised learning? Give one benefit and drawback for supervised and unsupervised learning, respectively.
Solution to Question 2
`1. Supervised Learning: In supervised Machine Learning, the algorithm is trained on a dataset that is labeled, meaning each input is associated with corresponding target output. 2.Benefit: Supervised Machine learning is effective for tasks where the desired output is known, making it suitable for the tasks like classification and regression 3. Drawback: One drawback is that it relies heavily on the availability of the labeled data, which can be time consuming expensive to acquire, especially for large datasets or niche domains
- Unsupervised Learning:
- In Unsupervised learning, the algorithm is trained on unlabeled data, and its goal is to find is to find hidden patterns or structures within the data.
- Benefit: Unsupervised learning can uncover insights from data without the need for labeled examples, making it useful for exploratory data Analysis, clustering and anomaly detection.
- Drawback:Since unsupervised learning lacks explicit labels, evaluating the performance of the model can be more challenging compared to supervised learning. Additionally, interpreting the results may require human intervention to understand the discovered patterns or clusters.
Question 3 [18 pts]
This question relates to the College data set, which can be found in the file College.csv in the folder. It contains a number of variables for 777 different universities and colleges in the US. The variables are
- Private : Public/private indicator
- Apps : Number of applications received
- Accept : Number of applicants accepted
- Enroll : Number of new students enrolled
- Top10perc : New students from top 10 % of high school class
- Top25perc : New students from top 25 % of high school class
- F.Undergrad : Number of full-time undergraduates
- P.Undergrad : Number of part-time undergraduates
- Outstate : Out-of-state tuition
- Room.Board : Room and board costs
- Books : Estimated book costs
- Personal : Estimated personal spending
- PhD : Percent of faculty with Ph.D.’s
- Terminal : Percent of faculty with terminal degree
- S.F.Ratio : Student/faculty ratio
- perc.alumni : Percent of alumni who donate
- Expend : Instructional expenditure per student
- Grad.Rate : Graduation rate
Before reading the data into R, it can be viewed in Excel or a text editor.
- (a). [2 pts] Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data.
Solution to Question 3(a)
put your solution here
# Read.csv file for the college data
file_path <- "/Users/adityasrivatsav/Documents/EAS508/HW 1/College.csv"
College <- read.csv(file_path)(b). [2 pts] Look at the data using the View() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later. Try the following commands:
rownames(college) <- college[,1 ]View(college)
You should see that there is now a row.names column with the name of
each
university recorded. This means that R has given each row a name
corresponding to the appropriate university. R will not try to perform
calculations on the row names. However, we still need to eliminate the
first column in the data where the names are stored. Try
>college <- college[, -1]
> View(college)
Now you should see that the first data column is Private. Note that another column labeled row.names now appears before the Private column. However, this is not a data column but rather the name that R is giving to each row.
Solution to Question 3(b)
put your solution here
# Inspect the structure to confirm the correct column (assuming it's still the first column)
head(College)## X Private Apps Accept Enroll Top10perc Top25perc
## 1 Abilene Christian University Yes 1660 1232 721 23 52
## 2 Adelphi University Yes 2186 1924 512 16 29
## 3 Adrian College Yes 1428 1097 336 22 50
## 4 Agnes Scott College Yes 417 349 137 60 89
## 5 Alaska Pacific University Yes 193 146 55 16 44
## 6 Albertson College Yes 587 479 158 38 62
## F.Undergrad P.Undergrad Outstate Room.Board Books Personal PhD Terminal
## 1 2885 537 7440 3300 450 2200 70 78
## 2 2683 1227 12280 6450 750 1500 29 30
## 3 1036 99 11250 3750 400 1165 53 66
## 4 510 63 12960 5450 450 875 92 97
## 5 249 869 7560 4120 800 1500 76 72
## 6 678 41 13500 3335 500 675 67 73
## S.F.Ratio perc.alumni Expend Grad.Rate
## 1 18.1 12 7041 60
## 2 12.2 16 10527 56
## 3 12.9 30 8735 54
## 4 7.7 37 19016 59
## 5 11.9 2 10922 15
## 6 9.4 11 9727 55# Assuming the first column is correct and contains unique university names
# Let's ensure uniqueness
if(!anyDuplicated(College[,1])) {
rownames(College) <- as.character(College[,1])
College <- College[, -1] # Remove the first column after setting row names
} else {
print("The first column contains duplicate values. Please check the data.")
}
# Now, you can safely use View(college) to inspect the modified dataframe
View(College)(c).
- (i). [2 pts] Use the
summary()function to produce a numerical summary of the variables in the data set.
- (i). [2 pts] Use the
summary(College)## Private Apps Accept Enroll
## Length:777 Min. : 81 Min. : 72 Min. : 35
## Class :character 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242
## Mode :character Median : 1558 Median : 1110 Median : 434
## Mean : 3002 Mean : 2019 Mean : 780
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902
## Max. :48094 Max. :26330 Max. :6392
## Top10perc Top25perc F.Undergrad P.Undergrad
## Min. : 1.00 Min. : 9.0 Min. : 139 Min. : 1.0
## 1st Qu.:15.00 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0
## Median :23.00 Median : 54.0 Median : 1707 Median : 353.0
## Mean :27.56 Mean : 55.8 Mean : 3700 Mean : 855.3
## 3rd Qu.:35.00 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0
## Max. :96.00 Max. :100.0 Max. :31643 Max. :21836.0
## Outstate Room.Board Books Personal
## Min. : 2340 Min. :1780 Min. : 96.0 Min. : 250
## 1st Qu.: 7320 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850
## Median : 9990 Median :4200 Median : 500.0 Median :1200
## Mean :10441 Mean :4358 Mean : 549.4 Mean :1341
## 3rd Qu.:12925 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700
## Max. :21700 Max. :8124 Max. :2340.0 Max. :6800
## PhD Terminal S.F.Ratio perc.alumni
## Min. : 8.00 Min. : 24.0 Min. : 2.50 Min. : 0.00
## 1st Qu.: 62.00 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00
## Median : 75.00 Median : 82.0 Median :13.60 Median :21.00
## Mean : 72.66 Mean : 79.7 Mean :14.09 Mean :22.74
## 3rd Qu.: 85.00 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00
## Max. :103.00 Max. :100.0 Max. :39.80 Max. :64.00
## Expend Grad.Rate
## Min. : 3186 Min. : 10.00
## 1st Qu.: 6751 1st Qu.: 53.00
## Median : 8377 Median : 65.00
## Mean : 9660 Mean : 65.46
## 3rd Qu.:10830 3rd Qu.: 78.00
## Max. :56233 Max. :118.00- (ii). [2 pts] Use the
pairs()function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10]. Briefly state your observations.
#Read the csv file
data <- read.csv("College.csv")
#Summarize the data
summary(data)## X Private Apps Accept
## Length:777 Length:777 Min. : 81 Min. : 72
## Class :character Class :character 1st Qu.: 776 1st Qu.: 604
## Mode :character Mode :character Median : 1558 Median : 1110
## Mean : 3002 Mean : 2019
## 3rd Qu.: 3624 3rd Qu.: 2424
## Max. :48094 Max. :26330
## Enroll Top10perc Top25perc F.Undergrad
## Min. : 35 Min. : 1.00 Min. : 9.0 Min. : 139
## 1st Qu.: 242 1st Qu.:15.00 1st Qu.: 41.0 1st Qu.: 992
## Median : 434 Median :23.00 Median : 54.0 Median : 1707
## Mean : 780 Mean :27.56 Mean : 55.8 Mean : 3700
## 3rd Qu.: 902 3rd Qu.:35.00 3rd Qu.: 69.0 3rd Qu.: 4005
## Max. :6392 Max. :96.00 Max. :100.0 Max. :31643
## P.Undergrad Outstate Room.Board Books
## Min. : 1.0 Min. : 2340 Min. :1780 Min. : 96.0
## 1st Qu.: 95.0 1st Qu.: 7320 1st Qu.:3597 1st Qu.: 470.0
## Median : 353.0 Median : 9990 Median :4200 Median : 500.0
## Mean : 855.3 Mean :10441 Mean :4358 Mean : 549.4
## 3rd Qu.: 967.0 3rd Qu.:12925 3rd Qu.:5050 3rd Qu.: 600.0
## Max. :21836.0 Max. :21700 Max. :8124 Max. :2340.0
## Personal PhD Terminal S.F.Ratio
## Min. : 250 Min. : 8.00 Min. : 24.0 Min. : 2.50
## 1st Qu.: 850 1st Qu.: 62.00 1st Qu.: 71.0 1st Qu.:11.50
## Median :1200 Median : 75.00 Median : 82.0 Median :13.60
## Mean :1341 Mean : 72.66 Mean : 79.7 Mean :14.09
## 3rd Qu.:1700 3rd Qu.: 85.00 3rd Qu.: 92.0 3rd Qu.:16.50
## Max. :6800 Max. :103.00 Max. :100.0 Max. :39.80
## perc.alumni Expend Grad.Rate
## Min. : 0.00 Min. : 3186 Min. : 10.00
## 1st Qu.:13.00 1st Qu.: 6751 1st Qu.: 53.00
## Median :21.00 Median : 8377 Median : 65.00
## Mean :22.74 Mean : 9660 Mean : 65.46
## 3rd Qu.:31.00 3rd Qu.:10830 3rd Qu.: 78.00
## Max. :64.00 Max. :56233 Max. :118.00#Showing first 10 columns as the matrix
pairs(data[, sapply(data[1:10], is.numeric)])
- (iii). [3 pts] Use the
plot()function to produce side-by-side boxplots of Outstate versus Private. Briefly state your observations.
boxplot(Outstate ~ Private, data = data,
xlab = "Private",
ylab = "Outstate",
main = "Boxplot of Outstate by Private",
col = c("blue","green"))
- (iv).[2 pts] Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10 % of their high school classes exceeds 50 %.
> Elite <- rep("No", nrow(college))
> Elite[college$Top10perc > 50] <- "Yes"
> Elite <- as.factor(Elite)
> college <- data.frame(college , Elite)
Use the summary() function to see how many elite
universities there are. Now use the plot() function to
produce side-by-side boxplots of Outstate versus Elite.
Elite <- rep("No", nrow(College))
Elite[College$Top10perc > 50] <- "Yes"
Elite <- as.factor(Elite)
#Add Elite Variables to the College DataFrame
College <- data.frame(College, Elite)
#Summary of Elite Universities
summary(College$Elite)## No Yes
## 699 78# Plot side-by-side boxplots of Outstate versus Elite
boxplot(Outstate ~ Elite,
data = College,
xlab = "Elite",
ylab = "Outstate",
main = "Boxplot of Outstate by Elite",
col = c("blue", "green"))
- (v)[2 pts] Use the hist() function to produce some histograms with
differing numbers of bins for a few of the quantitative variables. You
may find the command
par(mfrow = c(2, 2))useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways.
# Set up the plot window to display four plots simultaneously in 2 * 2 Grid
par(mfrow = c(2, 2))
hist(College$Apps, breaks = 10, main = "Histogram of Apps (10 bins)")
hist(College$Accept, breaks = 20, main = "Histogram of Accept (20 bins)")
hist(College$Enroll, breaks = 30, main = "Histogram of Enroll (30 bins)")
hist(College$Outstate, breaks = 40, main = "Histogram of OutState (40 bins)")
- (vi)[3 pts]. Continue exploring the data, and provide a brief summary of what you discover.
#university names with the most students in the top 10% of the class
row.names(College)[which.max(College$Top10perc)]## [1] "Massachusetts Institute of Technology"acceptance_rate <-College$Accept / College$Apps
#Lowest Acceptance Rate
row.names(College)[which.min(College$Top10perc)]## [1] "Center for Creative Studies"#Highest Acceptance Rate
row.names(College)[which.max(College$Top10perc)]## [1] "Massachusetts Institute of Technology"plot(Grad.Rate ~ Outstate, data = College)
#College with Low Acceptance Raate
plot(S.F.Ratio ~ I(Accept/Apps), data = College)
#The highest Graduation Rate
plot(Grad.Rate ~ Top10perc, data = College)
Question 4 [16 pts]
This exercise involves the Boston housing data set.
- (a).[2 pts] To begin, load in the Boston data set. The Boston data set is part of the ISLR2 library.
> library(ISLR2)
Now the data set is contained in the object Boston.
> Boston
Read about the data set:
> ?Boston
How many rows are in this data set? How many columns? What do the rows and columns represent?
library(ISLR2)
data(Boston)
nrow(Boston)## [1] 506ncol(Boston)## [1] 13?Boston
str(Boston)## 'data.frame': 506 obs. of 13 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...- (b).[2 pts] Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings.
pairs(Boston)
- (c).[2 pts] Are any of the predictors associated with per capita crime rate? If so, explain the relationship.
plot(crim ~ age, data = Boston, log = "xy")
#Closer to work area crime rate
plot(crim ~ dis, data = Boston, log = "xy")
#Higher index of accessibility to radial highways, more crime
plot(crim ~ rad, data = Boston, log = "xy")
#as box plots, since rad appears categorial
plot(crim ~ as.factor(rad),
log = "y",
data = Boston,
xlab = "Accessibility to radial Highways",
ylab = "log of crime")
#Tax is higher, crime is more
plot(crim ~ tax, data = Boston, log = "xy")
# Higher Pupil:teacher ratio, more crime
plot(crim ~ ptratio, log = "xy", data = Boston)
#Correlations
cor(Boston)## crim zn indus chas nox
## crim 1.00000000 -0.20046922 0.40658341 -0.055891582 0.42097171
## zn -0.20046922 1.00000000 -0.53382819 -0.042696719 -0.51660371
## indus 0.40658341 -0.53382819 1.00000000 0.062938027 0.76365145
## chas -0.05589158 -0.04269672 0.06293803 1.000000000 0.09120281
## nox 0.42097171 -0.51660371 0.76365145 0.091202807 1.00000000
## rm -0.21924670 0.31199059 -0.39167585 0.091251225 -0.30218819
## age 0.35273425 -0.56953734 0.64477851 0.086517774 0.73147010
## dis -0.37967009 0.66440822 -0.70802699 -0.099175780 -0.76923011
## rad 0.62550515 -0.31194783 0.59512927 -0.007368241 0.61144056
## tax 0.58276431 -0.31456332 0.72076018 -0.035586518 0.66802320
## ptratio 0.28994558 -0.39167855 0.38324756 -0.121515174 0.18893268
## lstat 0.45562148 -0.41299457 0.60379972 -0.053929298 0.59087892
## medv -0.38830461 0.36044534 -0.48372516 0.175260177 -0.42732077
## rm age dis rad tax ptratio
## crim -0.21924670 0.35273425 -0.37967009 0.625505145 0.58276431 0.2899456
## zn 0.31199059 -0.56953734 0.66440822 -0.311947826 -0.31456332 -0.3916785
## indus -0.39167585 0.64477851 -0.70802699 0.595129275 0.72076018 0.3832476
## chas 0.09125123 0.08651777 -0.09917578 -0.007368241 -0.03558652 -0.1215152
## nox -0.30218819 0.73147010 -0.76923011 0.611440563 0.66802320 0.1889327
## rm 1.00000000 -0.24026493 0.20524621 -0.209846668 -0.29204783 -0.3555015
## age -0.24026493 1.00000000 -0.74788054 0.456022452 0.50645559 0.2615150
## dis 0.20524621 -0.74788054 1.00000000 -0.494587930 -0.53443158 -0.2324705
## rad -0.20984667 0.45602245 -0.49458793 1.000000000 0.91022819 0.4647412
## tax -0.29204783 0.50645559 -0.53443158 0.910228189 1.00000000 0.4608530
## ptratio -0.35550149 0.26151501 -0.23247054 0.464741179 0.46085304 1.0000000
## lstat -0.61380827 0.60233853 -0.49699583 0.488676335 0.54399341 0.3740443
## medv 0.69535995 -0.37695457 0.24992873 -0.381626231 -0.46853593 -0.5077867
## lstat medv
## crim 0.4556215 -0.3883046
## zn -0.4129946 0.3604453
## indus 0.6037997 -0.4837252
## chas -0.0539293 0.1752602
## nox 0.5908789 -0.4273208
## rm -0.6138083 0.6953599
## age 0.6023385 -0.3769546
## dis -0.4969958 0.2499287
## rad 0.4886763 -0.3816262
## tax 0.5439934 -0.4685359
## ptratio 0.3740443 -0.5077867
## lstat 1.0000000 -0.7376627
## medv -0.7376627 1.0000000- (d)[2 pts] Do any of the census tracts of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor.
par(mfrow = c(1, 3))
hist(Boston$crim[Boston$crim > 1], breaks = 25)
hist(Boston$tax, breaks = 25)
hist(Boston$ptratio, breaks = 25)
- (e)[1 pt] How many of the census tracts in this data set bound the Charles river?
sum(Boston$chas == 1)## [1] 35- (f)[1 pt] What is the median pupil-teacher ratio among the towns in this data set?
median(Boston$ptratio)## [1] 19.05- (g)[3 pts] Which census tract of Boston has lowest median value of owneroccupied homes? What are the values of the other predictors for that census tract, and how do those values compare to the overall ranges for those predictors? Comment on your findings.
t(subset(Boston, medv == min(medv)))## 399 406
## crim 38.3518 67.9208
## zn 0.0000 0.0000
## indus 18.1000 18.1000
## chas 0.0000 0.0000
## nox 0.6930 0.6930
## rm 5.4530 5.6830
## age 100.0000 100.0000
## dis 1.4896 1.4254
## rad 24.0000 24.0000
## tax 666.0000 666.0000
## ptratio 20.2000 20.2000
## lstat 30.5900 22.9800
## medv 5.0000 5.0000summary(Boston)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08205 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio lstat
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 1.73
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.: 6.95
## Median : 5.000 Median :330.0 Median :19.05 Median :11.36
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :12.65
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:16.95
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :37.97
## medv
## Min. : 5.00
## 1st Qu.:17.02
## Median :21.20
## Mean :22.53
## 3rd Qu.:25.00
## Max. :50.00- (h)[3 pts] In this data set, how many of the census tracts average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the census tracts that average more than eight rooms per dwelling.
sum(Boston$rm > 7)## [1] 64sum(Boston$rm > 8)## [1] 13summary(subset(Boston, rm > 8))## crim zn indus chas
## Min. :0.02009 Min. : 0.00 Min. : 2.680 Min. :0.0000
## 1st Qu.:0.33147 1st Qu.: 0.00 1st Qu.: 3.970 1st Qu.:0.0000
## Median :0.52014 Median : 0.00 Median : 6.200 Median :0.0000
## Mean :0.71879 Mean :13.62 Mean : 7.078 Mean :0.1538
## 3rd Qu.:0.57834 3rd Qu.:20.00 3rd Qu.: 6.200 3rd Qu.:0.0000
## Max. :3.47428 Max. :95.00 Max. :19.580 Max. :1.0000
## nox rm age dis
## Min. :0.4161 Min. :8.034 Min. : 8.40 Min. :1.801
## 1st Qu.:0.5040 1st Qu.:8.247 1st Qu.:70.40 1st Qu.:2.288
## Median :0.5070 Median :8.297 Median :78.30 Median :2.894
## Mean :0.5392 Mean :8.349 Mean :71.54 Mean :3.430
## 3rd Qu.:0.6050 3rd Qu.:8.398 3rd Qu.:86.50 3rd Qu.:3.652
## Max. :0.7180 Max. :8.780 Max. :93.90 Max. :8.907
## rad tax ptratio lstat medv
## Min. : 2.000 Min. :224.0 Min. :13.00 Min. :2.47 Min. :21.9
## 1st Qu.: 5.000 1st Qu.:264.0 1st Qu.:14.70 1st Qu.:3.32 1st Qu.:41.7
## Median : 7.000 Median :307.0 Median :17.40 Median :4.14 Median :48.3
## Mean : 7.462 Mean :325.1 Mean :16.36 Mean :4.31 Mean :44.2
## 3rd Qu.: 8.000 3rd Qu.:307.0 3rd Qu.:17.40 3rd Qu.:5.12 3rd Qu.:50.0
## Max. :24.000 Max. :666.0 Max. :20.20 Max. :7.44 Max. :50.0summary(Boston)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08205 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio lstat
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 1.73
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.: 6.95
## Median : 5.000 Median :330.0 Median :19.05 Median :11.36
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :12.65
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:16.95
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :37.97
## medv
## Min. : 5.00
## 1st Qu.:17.02
## Median :21.20
## Mean :22.53
## 3rd Qu.:25.00
## Max. :50.00Question 5. [6 pts]
Suppose we have a data set with five predictors, \(X1 = \text{GPA}, X2 =IQ, X3 = \text{Level (1 for College and 0 for High School)}, X4 =\text{Interaction between GPA and IQ, and }X5 = \text{Interaction between GPA and Level.}\) The response is starting salary after graduation (in thousands of dollars). Suppose we use least squares to fit the model, and get \(\hat{\beta}_0 = 50, \hat{\beta}_1 = 20, \hat{\beta}_2 = 0.07, \hat{\beta}_3 = 35, \hat{\beta}_4 = 0.01, \hat{\beta}_5 = −10\).
- (a)[3 pts] Predict the salary of a college graduate with IQ of \(110\) and a GPA of \(4.0\).
#Given Coefficients
beta_0 <- 50
beta_1 <- 20
beta_2 <- 0.07
beta_3 <- 35
beta_4 <- 0.01
beta_5 <- -10
#Given Predictor Values
GPA <- 4.0
IQ <- 110
Level <- 1
# Compute Interaction terms
Interaction_GPA_IQ <- GPA * IQ
Interaction_GPA_Level <- GPA * Level
# Compute Predicted Salary
predicted_salary <- beta_0 + beta_1 * GPA + beta_2 * IQ + beta_3 * Level + beta_4 * Interaction_GPA_IQ + beta_5 * Interaction_GPA_Level
#Print Predicted Salary
print(predicted_salary)## [1] 137.1- (b)[3 pts] True or false: Since the coefficient for the GPA/IQ interaction term is very small, there is very little evidence of an interaction effect. Justify your answer. #Solution False. The size of the coefficient for the GPA/IQ interaction term alone cannot determine the presence or absence of an interaction effect. While a small coefficient might suggest a weaker interaction effect, it doesn’t necessarily imply the absence of interaction. 1.In linear regression, the significance of coefficients is assessed through hypothesis testing, typically using the associated p-values. To determine the significance of the interaction effect between GPA and IQ on starting salary, we need to check the p-value associated with the coefficient estimate for the GPA/IQ interaction term (\(\hat{\beta}_4\)).
2.If the p-value is sufficiently small (typically less than a chosen significance level, e.g., 0.05), then we can reject the null hypothesis that there is no interaction effect. In this case, we would have evidence supporting the presence of an interaction effect between GPA and IQ on the starting salary.
3.Therefore, whether there is evidence of an interaction effect cannot be determined solely by the size of the coefficient for the interaction term; the significance of this coefficient (through its associated p-value) is crucial in making such a determination.
Question 6. [34 pts]
This question involves the use of multiple linear regression on the Auto data set.
data(Auto)
data<-Auto
head(data)## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18 8 307 130 3504 12.0 70 1
## 2 15 8 350 165 3693 11.5 70 1
## 3 18 8 318 150 3436 11.0 70 1
## 4 16 8 304 150 3433 12.0 70 1
## 5 17 8 302 140 3449 10.5 70 1
## 6 15 8 429 198 4341 10.0 70 1
## name
## 1 chevrolet chevelle malibu
## 2 buick skylark 320
## 3 plymouth satellite
## 4 amc rebel sst
## 5 ford torino
## 6 ford galaxie 500- (a).[3 pts] Produce a scatterplot matrix which includes all numeric variables in the data set. Please give the interpretation of the plot.
dataAuto <- read.csv("/Users/adityasrivatsav/Documents/EAS508/HW 1/Auto.csv",na.strings = "?")
dataAuto <- na.omit(dataAuto)
dim(dataAuto)## [1] 392 9#summary of the data Auto
summary(dataAuto)## mpg cylinders displacement horsepower weight
## Min. : 9.00 Min. :3.000 Min. : 68.0 Min. : 46.0 Min. :1613
## 1st Qu.:17.00 1st Qu.:4.000 1st Qu.:105.0 1st Qu.: 75.0 1st Qu.:2225
## Median :22.75 Median :4.000 Median :151.0 Median : 93.5 Median :2804
## Mean :23.45 Mean :5.472 Mean :194.4 Mean :104.5 Mean :2978
## 3rd Qu.:29.00 3rd Qu.:8.000 3rd Qu.:275.8 3rd Qu.:126.0 3rd Qu.:3615
## Max. :46.60 Max. :8.000 Max. :455.0 Max. :230.0 Max. :5140
## acceleration year origin name
## Min. : 8.00 Min. :70.00 Min. :1.000 Length:392
## 1st Qu.:13.78 1st Qu.:73.00 1st Qu.:1.000 Class :character
## Median :15.50 Median :76.00 Median :1.000 Mode :character
## Mean :15.54 Mean :75.98 Mean :1.577
## 3rd Qu.:17.02 3rd Qu.:79.00 3rd Qu.:2.000
## Max. :24.80 Max. :82.00 Max. :3.000pairs(dataAuto[, sapply(dataAuto, is.numeric)])
- (b) [3 pts] Compute the matrix of correlations between the variables.
You will need to exclude the name variable, which is qualitative.
Explain your discoveries, find the top 1 predictors.
# Correlation Matrix
correlation_matrix <- cor(dataAuto[, sapply(dataAuto, is.numeric)])
# Find the top predictor
top_predictor <- colnames(correlation_matrix)[which.max(correlation_matrix["mpg", ])]
# Print correlation matrix
print(correlation_matrix)## mpg cylinders displacement horsepower weight
## mpg 1.0000000 -0.7776175 -0.8051269 -0.7784268 -0.8322442
## cylinders -0.7776175 1.0000000 0.9508233 0.8429834 0.8975273
## displacement -0.8051269 0.9508233 1.0000000 0.8972570 0.9329944
## horsepower -0.7784268 0.8429834 0.8972570 1.0000000 0.8645377
## weight -0.8322442 0.8975273 0.9329944 0.8645377 1.0000000
## acceleration 0.4233285 -0.5046834 -0.5438005 -0.6891955 -0.4168392
## year 0.5805410 -0.3456474 -0.3698552 -0.4163615 -0.3091199
## origin 0.5652088 -0.5689316 -0.6145351 -0.4551715 -0.5850054
## acceleration year origin
## mpg 0.4233285 0.5805410 0.5652088
## cylinders -0.5046834 -0.3456474 -0.5689316
## displacement -0.5438005 -0.3698552 -0.6145351
## horsepower -0.6891955 -0.4163615 -0.4551715
## weight -0.4168392 -0.3091199 -0.5850054
## acceleration 1.0000000 0.2903161 0.2127458
## year 0.2903161 1.0000000 0.1815277
## origin 0.2127458 0.1815277 1.0000000# Print top predictor
print(paste("Top Predictor:", top_predictor))## [1] "Top Predictor: mpg"- (c)[6 pts] perform a simple linear regression use MPG as response and the top predictor. Produce diagnostic plots of the linear regression fit (similar as the ones we showed on class to check the assumptions of linear regression: linearity, normality, constant variance). Interpret your discoveries.
dataAuto <- read.csv("/Users/adityasrivatsav/Documents/EAS508/HW 1/Auto.csv",na.strings = "?")
dataAuto <- na.omit(dataAuto)
# Calculate correlations between "MPG" and other variables
correlations <- cor(dataAuto[, -9], dataAuto$mpg)
# Find the top predictor with the highest absolute correlation
top_predictor <- names(which.max(abs(correlations)))
# Fit linear regression model
lm_model <- lm(mpg ~ ., data = dataAuto)
# Generate diagnostic plots
par(mfrow = c(2, 2))
plot(lm_model)## Warning: not plotting observations with leverage one:
## 2, 3, 4, 5, 10, 11, 13, 15, 20, 22, 23, 24, 26, 27, 28, 29, 31, 34, 36, 39, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 58, 59, 61, 66, 67, 68, 70, 71, 73, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 89, 90, 93, 94, 95, 96, 98, 102, 104, 105, 108, 110, 111, 113, 114, 115, 116, 121, 124, 128, 136, 137, 140, 147, 150, 151, 153, 156, 157, 160, 163, 164, 165, 169, 175, 178, 181, 183, 185, 187, 195, 198, 199, 200, 201, 203, 206, 207, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 226, 227, 228, 230, 231, 232, 233, 234, 235, 237, 240, 241, 242, 243, 244, 245, 246, 249, 250, 251, 253, 254, 255, 257, 258, 260, 262, 263, 264, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 285, 286, 287, 290, 291, 292, 293, 294, 295, 296, 297, 300, 301, 303, 304, 306, 309, 311, 313, 316, 317, 319, 321, 324, 325, 326, 327, 328, 330, 331, 332, 333, 337, 340, 341, 342, 344, 345, 346, 347, 348, 349, 350, 351, 353, 355, 356, 357, 358, 360, 361, 362, 363, 364, 365, 366, 367, 369, 370, 371, 372, 373, 374, 375, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
(d)[4 pts] Use the
lm()function to perform a multiple linear regression with mpg as the response and all other variables except name as the predictors. Use the summary() function to print the results. Comment on the output. For instance:- Is there a relationship between the predictors and the response?
- Which predictors appear to have a statistically significant relationship to the response?
- What does the coefficient for the year variable suggest?
# Perform multiple linear Regression
lm_model <- lm(mpg ~ . - name, data = dataAuto)
# Print summary of the regression results
summary(lm_model)##
## Call:
## lm(formula = mpg ~ . - name, data = dataAuto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5903 -2.1565 -0.1169 1.8690 13.0604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.218435 4.644294 -3.707 0.00024 ***
## cylinders -0.493376 0.323282 -1.526 0.12780
## displacement 0.019896 0.007515 2.647 0.00844 **
## horsepower -0.016951 0.013787 -1.230 0.21963
## weight -0.006474 0.000652 -9.929 < 2e-16 ***
## acceleration 0.080576 0.098845 0.815 0.41548
## year 0.750773 0.050973 14.729 < 2e-16 ***
## origin 1.426141 0.278136 5.127 4.67e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.328 on 384 degrees of freedom
## Multiple R-squared: 0.8215, Adjusted R-squared: 0.8182
## F-statistic: 252.4 on 7 and 384 DF, p-value: < 2.2e-16- (e)[5 pts] Produce diagnostic plots of the linear regression fit. Comment on any problems you see with the fit. Do the residual plots suggest any unusually large outliers? Does the leverage plot identify any observations with unusually high leverage?
# Produce diagnostic plots
par(mfrow = c(2,2))
plot(lm_model)
- [5 pts] Fit a multiple linear regression model called model_tops using MPG as the response and the top 3 predicting variables with the strongest relationship with MPG. Compare the coefficients of the 3 predictor in model_tops with the model that used all numeric predictors, which ones are larger? Why?
# Extract coefficients from the previous model
coefficients_all <- coef(lm_model)
# Find the top 3 predictors with the strongest relationship with MPG
top_3_predictors <- names(sort(abs(coefficients_all[-1]), decreasing = TRUE)[1:3])
# Create a new model using only the top 3 predictors
model_tops <- lm(mpg ~ ., data = dataAuto[, c("mpg", top_3_predictors)])
# Compare coefficients
coefficients_model_tops <- coef(model_tops)
coefficients_all## (Intercept) cylinders displacement horsepower weight
## -17.218434622 -0.493376319 0.019895644 -0.016951144 -0.006474043
## acceleration year origin
## 0.080575838 0.750772678 1.426140495coefficients_model_tops## (Intercept) origin year cylinders
## -23.2944368 1.8367029 0.7570703 -2.4995084- (g)[3 pts] Use the * and : symbols to fit linear regression models with interaction effects. Do any interactions appear to be statistically significant?
# Fit Linear Regression model with interaction effects
model_interaction <- lm(mpg ~ .* ., data = dataAuto)
# Check for significiant interactions
summary(model_interaction)##
## Call:
## lm(formula = mpg ~ . * ., data = dataAuto)
##
## Residuals:
## ALL 392 residuals are 0: no residual degrees of freedom!
##
## Coefficients: (2037 not defined because of singularities)
## Estimate Std. Error
## (Intercept) -3.383e+03 NaN
## cylinders -1.631e+03 NaN
## displacement -4.019e+01 NaN
## horsepower 6.561e+00 NaN
## weight -8.695e-01 NaN
## acceleration -7.249e+00 NaN
## year -2.886e+00 NaN
## origin 5.432e+03 NaN
## nameamc ambassador dpl -1.169e+03 NaN
## nameamc ambassador sst 1.955e+03 NaN
## nameamc concord 5.608e+03 NaN
## nameamc concord d/l 5.109e+03 NaN
## nameamc concord dl 6 5.896e+03 NaN
## nameamc gremlin 7.658e+03 NaN
## nameamc hornet 8.524e+03 NaN
## nameamc hornet sportabout (sw) 5.247e+03 NaN
## nameamc matador 1.511e+04 NaN
## nameamc matador (sw) 2.211e+03 NaN
## nameamc pacer 5.889e+03 NaN
## nameamc pacer d/l 5.703e+03 NaN
## nameamc rebel sst 1.954e+03 NaN
## nameamc spirit dl 5.554e+03 NaN
## nameaudi 100 ls -7.027e+01 NaN
## nameaudi 100ls 5.207e+03 NaN
## nameaudi 4000 -2.254e+01 NaN
## nameaudi 5000 2.854e+02 NaN
## nameaudi 5000s (diesel) 6.224e+02 NaN
## nameaudi fox -4.509e+01 NaN
## namebmw 2002 -1.445e+02 NaN
## namebmw 320i -1.937e+02 NaN
## namebuick century 4.711e+03 NaN
## namebuick century 350 2.370e+02 NaN
## namebuick century limited 5.674e+03 NaN
## namebuick century luxus (sw) 1.202e+03 NaN
## namebuick century special 5.557e+03 NaN
## namebuick electra 225 custom -3.706e+03 NaN
## namebuick estate wagon (sw) 1.930e+04 NaN
## namebuick lesabre custom 9.829e+02 NaN
## namebuick opel isuzu deluxe 5.494e+03 NaN
## namebuick regal sport coupe (turbo) 4.169e+03 NaN
## namebuick skyhawk 5.408e+03 NaN
## namebuick skylark 6.425e+03 NaN
## namebuick skylark 320 5.018e+02 NaN
## namebuick skylark limited 5.760e+03 NaN
## namecadillac eldorado 1.791e+03 NaN
## namecadillac seville 1.084e+02 NaN
## namecapri ii 5.602e+03 NaN
## namechevroelt chevelle malibu 5.682e+03 NaN
## namechevrolet bel air 1.305e+03 NaN
## namechevrolet camaro 5.770e+03 NaN
## namechevrolet caprice classic 1.101e+04 NaN
## namechevrolet cavalier 5.338e+03 NaN
## namechevrolet cavalier 2-door 5.378e+03 NaN
## namechevrolet cavalier wagon 5.330e+03 NaN
## namechevrolet chevelle concours (sw) 2.445e+03 NaN
## namechevrolet chevelle malibu 1.546e+04 NaN
## namechevrolet chevelle malibu classic 1.659e+04 NaN
## namechevrolet chevette 5.532e+03 NaN
## namechevrolet citation 5.798e+03 NaN
## namechevrolet concours 5.421e+03 NaN
## namechevrolet impala 1.354e+04 NaN
## namechevrolet malibu 1.986e+04 NaN
## namechevrolet malibu classic (sw) 3.306e+03 NaN
## namechevrolet monte carlo -9.065e+01 NaN
## namechevrolet monte carlo landau 1.316e+04 NaN
## namechevrolet monte carlo s 1.208e+03 NaN
## namechevrolet monza 2+2 3.748e+03 NaN
## namechevrolet nova 7.334e+03 NaN
## namechevrolet nova custom 5.634e+03 NaN
## namechevrolet vega 6.945e+03 NaN
## namechevrolet vega (sw) 5.933e+03 NaN
## namechevrolet vega 2300 5.629e+03 NaN
## namechevrolet woody 5.615e+03 NaN
## namechevy c10 1.195e+03 NaN
## namechevy c20 3.243e+02 NaN
## namechevy s-10 5.503e+03 NaN
## namechrysler cordoba -1.303e+03 NaN
## namechrysler lebaron medallion 5.766e+03 NaN
## namechrysler lebaron salon 6.033e+03 NaN
## namechrysler lebaron town @ country (sw) 8.099e+02 NaN
## namechrysler new yorker brougham -3.026e+03 NaN
## namechrysler newport royal -1.285e+03 NaN
## namedatsun 1200 -5.346e+03 NaN
## namedatsun 200-sx -5.467e+03 NaN
## namedatsun 200sx -5.499e+03 NaN
## namedatsun 210 -5.355e+03 NaN
## namedatsun 210 mpg -5.406e+03 NaN
## namedatsun 280-zx -5.360e+03 NaN
## namedatsun 310 -5.425e+03 NaN
## namedatsun 310 gx -5.415e+03 NaN
## namedatsun 510 -5.453e+03 NaN
## namedatsun 510 (sw) -5.448e+03 NaN
## namedatsun 510 hatchback -5.443e+03 NaN
## namedatsun 610 -5.465e+03 NaN
## namedatsun 710 -5.252e+03 NaN
## namedatsun 810 -4.920e+03 NaN
## namedatsun 810 maxima -5.012e+03 NaN
## namedatsun b-210 -5.410e+03 NaN
## namedatsun b210 -5.404e+03 NaN
## namedatsun b210 gx -5.409e+03 NaN
## namedatsun f-10 hatchback -5.404e+03 NaN
## namedatsun pl510 -5.417e+03 NaN
## namedodge aries se 5.662e+03 NaN
## namedodge aries wagon (sw) 5.771e+03 NaN
## namedodge aspen 7.946e+03 NaN
## namedodge aspen 6 5.453e+03 NaN
## namedodge aspen se 5.744e+03 NaN
## namedodge challenger se -4.584e+02 NaN
## namedodge charger 2.2 5.667e+03 NaN
## namedodge colt 5.585e+03 NaN
## namedodge colt (sw) 5.376e+03 NaN
## namedodge colt hardtop 5.376e+03 NaN
## namedodge colt hatchback custom 5.428e+03 NaN
## namedodge colt m/m 5.366e+03 NaN
## namedodge coronet brougham 1.661e+03 NaN
## namedodge coronet custom 1.647e+03 NaN
## namedodge coronet custom (sw) 1.677e+03 NaN
## namedodge d100 1.638e+03 NaN
## namedodge d200 -2.089e+02 NaN
## namedodge dart custom 1.638e+03 NaN
## namedodge diplomat 1.915e+03 NaN
## namedodge magnum xe 1.942e+03 NaN
## namedodge monaco (sw) -3.828e+02 NaN
## namedodge monaco brougham 1.801e+03 NaN
## namedodge omni 5.478e+03 NaN
## namedodge rampage 5.664e+03 NaN
## namedodge st. regis 2.058e+03 NaN
## namefiat 124 sport coupe -9.486e+01 NaN
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## namefiat 124b -3.710e+01 NaN
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## namefiat 131 -5.233e+01 NaN
## namefiat strada custom -1.021e+01 NaN
## namefiat x1.9 -4.174e+01 NaN
## nameford country -1.510e+02 NaN
## nameford country squire (sw) 1.277e+04 NaN
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## nameford f108 2.502e+03 NaN
## nameford f250 -1.385e+03 NaN
## nameford fairmont 5.669e+03 NaN
## nameford fairmont (auto) 6.013e+03 NaN
## nameford fairmont (man) 5.666e+03 NaN
## nameford fairmont 4 5.668e+03 NaN
## nameford fairmont futura 5.581e+03 NaN
## nameford fiesta 5.546e+03 NaN
## nameford futura 2.282e+03 NaN
## nameford galaxie 500 1.442e+04 NaN
## nameford gran torino 1.182e+04 NaN
## nameford gran torino (sw) 2.257e+03 NaN
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## nameford granada ghia 6.366e+03 NaN
## nameford granada gl 5.962e+03 NaN
## nameford granada l 5.344e+03 NaN
## nameford ltd 7.389e+03 NaN
## nameford ltd landau 2.515e+03 NaN
## nameford maverick 8.853e+03 NaN
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## nameford mustang gl 5.688e+03 NaN
## nameford mustang ii 2.479e+03 NaN
## nameford mustang ii 2+2 5.654e+03 NaN
## nameford pinto 5.331e+03 NaN
## nameford pinto (sw) 5.510e+03 NaN
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## nameford ranger 5.562e+03 NaN
## nameford thunderbird 1.115e+03 NaN
## nameford torino 2.243e+03 NaN
## nameford torino 500 5.944e+03 NaN
## namehi 1200d 4.598e+02 NaN
## namehonda accord -5.172e+03 NaN
## namehonda accord cvcc -5.400e+03 NaN
## namehonda accord lx -5.416e+03 NaN
## namehonda civic -5.238e+03 NaN
## namehonda civic (auto) -5.420e+03 NaN
## namehonda civic 1300 -5.416e+03 NaN
## namehonda civic 1500 gl -5.401e+03 NaN
## namehonda civic cvcc -5.495e+03 NaN
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## namemaxda glc deluxe -5.428e+03 NaN
## namemaxda rx3 -6.408e+03 NaN
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## namemazda glc 4 -5.416e+03 NaN
## namemazda glc custom -5.411e+03 NaN
## namemazda glc custom l -5.409e+03 NaN
## namemazda glc deluxe -5.438e+03 NaN
## namemazda rx-4 -6.486e+03 NaN
## namemazda rx-7 gs -6.476e+03 NaN
## namemazda rx2 coupe -6.447e+03 NaN
## namemercedes benz 300d 7.778e+02 NaN
## namemercedes-benz 240d 6.462e+02 NaN
## namemercedes-benz 280s -1.625e+02 NaN
## namemercury capri 2000 5.518e+03 NaN
## namemercury capri v6 6.032e+03 NaN
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## namemercury grand marquis 1.365e+03 NaN
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## namemercury marquis brougham -1.960e+03 NaN
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## namemercury monarch ghia 2.271e+03 NaN
## namemercury zephyr 6.027e+03 NaN
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## namenissan stanza xe -5.414e+03 NaN
## nameoldsmobile cutlass ciera (diesel) 5.866e+03 NaN
## nameoldsmobile cutlass ls 2.355e+03 NaN
## nameoldsmobile cutlass salon brougham 6.449e+03 NaN
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## nameoldsmobile delta 88 royale 7.959e+02 NaN
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## nameoldsmobile omega brougham 5.735e+03 NaN
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## nameoldsmobile vista cruiser 1.099e+02 NaN
## nameopel 1900 5.222e+02 NaN
## nameopel manta -7.449e+02 NaN
## namepeugeot 304 -4.408e+01 NaN
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## namepeugeot 504 (sw) 2.766e+01 NaN
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## nameplymouth custom suburb 3.020e+02 NaN
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## nameplymouth fury gran sedan 1.666e+03 NaN
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## nameplymouth satellite custom (sw) 1.659e+03 NaN
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## namepontiac catalina brougham -6.652e+02 NaN
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## namepontiac grand prix -2.772e+03 NaN
## namepontiac grand prix lj -9.457e+02 NaN
## namepontiac j2000 se hatchback 5.382e+03 NaN
## namepontiac lemans v6 5.312e+03 NaN
## namepontiac phoenix 5.756e+03 NaN
## namepontiac phoenix lj 5.592e+03 NaN
## namepontiac safari (sw) -3.725e+02 NaN
## namepontiac sunbird coupe 5.806e+03 NaN
## namepontiac ventura sj 5.456e+03 NaN
## namerenault 12 (sw) 3.431e+01 NaN
## namerenault 12tl -3.225e+01 NaN
## namerenault 5 gtl 2.011e+01 NaN
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## namesaab 99gle -3.066e+02 NaN
## namesaab 99le 8.744e+02 NaN
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## namesubaru dl -5.410e+03 NaN
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## nametoyota celica gt liftback -5.449e+03 NaN
## nametoyota corolla -5.263e+03 NaN
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## nametoyota corolla 1600 (sw) -5.416e+03 NaN
## nametoyota corolla liftback -5.426e+03 NaN
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## nametoyota corona liftback -5.412e+03 NaN
## nametoyota corona mark ii -5.456e+03 NaN
## nametoyota cressida -5.316e+03 NaN
## nametoyota mark ii -5.125e+03 NaN
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## nametoyota tercel -5.424e+03 NaN
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## namevolkswagen rabbit custom diesel 1.428e+02 NaN
## namevolkswagen rabbit l 6.214e+01 NaN
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## namevolvo 245 -1.239e+02 NaN
## namevolvo 264gl 5.503e+01 NaN
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## namevw rabbit c (diesel) 1.411e+02 NaN
## namevw rabbit custom NA NA
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## cylinders:horsepower -3.296e+00 NaN
## cylinders:weight 1.907e-01 NaN
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## cylinders:nameamc matador -1.210e+03 NaN
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## cylinders:namebuick skylark -1.423e+02 NaN
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## cylinders:namechevrolet cavalier 2-door NA NA
## cylinders:namechevrolet cavalier wagon NA NA
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## cylinders:namechevrolet chevelle malibu -1.635e+03 NaN
## cylinders:namechevrolet chevelle malibu classic -1.801e+03 NaN
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## cylinders:namechevrolet citation 3.483e+01 NaN
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## cylinders:namedatsun 200sx NA NA
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## cylinders:namedatsun 210 mpg NA NA
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## cylinders:namedatsun 510 (sw) NA NA
## cylinders:namedatsun 510 hatchback NA NA
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## cylinders:namedodge aspen 6 NA NA
## cylinders:namedodge aspen se NA NA
## cylinders:namedodge challenger se NA NA
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## cylinders:namedodge colt (sw) NA NA
## cylinders:namedodge colt hardtop NA NA
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## cylinders:namedodge colt m/m NA NA
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## cylinders:namedodge coronet custom NA NA
## cylinders:namedodge coronet custom (sw) NA NA
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## cylinders:namedodge d200 NA NA
## cylinders:namedodge dart custom NA NA
## cylinders:namedodge diplomat NA NA
## cylinders:namedodge magnum xe NA NA
## cylinders:namedodge monaco (sw) NA NA
## cylinders:namedodge monaco brougham NA NA
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## cylinders:namedodge rampage NA NA
## cylinders:namedodge st. regis NA NA
## cylinders:namefiat 124 sport coupe NA NA
## cylinders:namefiat 124 tc NA NA
## cylinders:namefiat 124b NA NA
## cylinders:namefiat 128 NA NA
## cylinders:namefiat 131 NA NA
## cylinders:namefiat strada custom NA NA
## cylinders:namefiat x1.9 NA NA
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## cylinders:nameford country squire (sw) NA NA
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## cylinders:nameford escort 4w NA NA
## cylinders:nameford f108 NA NA
## cylinders:nameford f250 NA NA
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## cylinders:nameford fairmont (auto) NA NA
## cylinders:nameford fairmont (man) NA NA
## cylinders:nameford fairmont 4 NA NA
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## cylinders:nameford fiesta NA NA
## cylinders:nameford futura NA NA
## cylinders:nameford galaxie 500 NA NA
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## cylinders:nameford gran torino (sw) NA NA
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## cylinders:nameford granada l NA NA
## cylinders:nameford ltd NA NA
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## cylinders:nameford mustang gl NA NA
## cylinders:nameford mustang ii NA NA
## cylinders:nameford mustang ii 2+2 NA NA
## cylinders:nameford pinto NA NA
## cylinders:nameford pinto (sw) NA NA
## cylinders:nameford pinto runabout NA NA
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## cylinders:nameford torino 500 NA NA
## cylinders:namehi 1200d NA NA
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## cylinders:namehonda accord cvcc NA NA
## cylinders:namehonda accord lx NA NA
## cylinders:namehonda civic NA NA
## cylinders:namehonda civic (auto) NA NA
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## cylinders:namemazda glc NA NA
## cylinders:namemazda glc 4 NA NA
## cylinders:namemazda glc custom NA NA
## cylinders:namemazda glc custom l NA NA
## cylinders:namemazda glc deluxe NA NA
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## cylinders:namemazda rx2 coupe NA NA
## cylinders:namemercedes benz 300d NA NA
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## cylinders:nameplymouth volare custom NA NA
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## cylinders:namepontiac phoenix lj NA NA
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## cylinders:namesaab 99gle NA NA
## cylinders:namesaab 99le NA NA
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## cylinders:nametoyota celica gt liftback NA NA
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## cylinders:nametoyota corolla 1200 NA NA
## cylinders:nametoyota corolla 1600 (sw) NA NA
## cylinders:nametoyota corolla liftback NA NA
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## cylinders:nametoyota tercel NA NA
## cylinders:nametoyouta corona mark ii (sw) NA NA
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## cylinders:namevolkswagen rabbit NA NA
## cylinders:namevolkswagen rabbit custom NA NA
## cylinders:namevolkswagen rabbit custom diesel NA NA
## cylinders:namevolkswagen rabbit l NA NA
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## cylinders:namevolvo 245 NA NA
## cylinders:namevolvo 264gl NA NA
## cylinders:namevolvo diesel NA NA
## cylinders:namevw dasher (diesel) NA NA
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## cylinders:namevw rabbit c (diesel) NA NA
## cylinders:namevw rabbit custom NA NA
## displacement:horsepower 9.741e-02 NaN
## displacement:weight -6.496e-03 NaN
## displacement:acceleration 4.453e-03 NaN
## displacement:year -1.747e-02 NaN
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## displacement:nameamc ambassador dpl NA NA
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## displacement:nameamc concord dl 6 NA NA
## displacement:nameamc gremlin -1.171e+01 NaN
## displacement:nameamc hornet -5.284e+00 NaN
## displacement:nameamc hornet sportabout (sw) NA NA
## displacement:nameamc matador -3.359e+00 NaN
## displacement:nameamc matador (sw) NA NA
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## displacement:nameamc spirit dl NA NA
## displacement:nameaudi 100 ls NA NA
## displacement:nameaudi 100ls -4.622e+01 NaN
## displacement:nameaudi 4000 NA NA
## displacement:nameaudi 5000 NA NA
## displacement:nameaudi 5000s (diesel) NA NA
## displacement:nameaudi fox NA NA
## displacement:namebmw 2002 NA NA
## displacement:namebmw 320i NA NA
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## displacement:namebuick century 350 NA NA
## displacement:namebuick century limited NA NA
## displacement:namebuick century luxus (sw) NA NA
## displacement:namebuick century special NA NA
## displacement:namebuick electra 225 custom NA NA
## displacement:namebuick estate wagon (sw) -5.250e+01 NaN
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## displacement:namebuick opel isuzu deluxe NA NA
## displacement:namebuick regal sport coupe (turbo) NA NA
## displacement:namebuick skyhawk NA NA
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## displacement:namebuick skylark 320 NA NA
## displacement:namebuick skylark limited NA NA
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## displacement:namechevrolet caprice classic -1.695e+01 NaN
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## displacement:namechevrolet cavalier 2-door NA NA
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## displacement:namechevrolet chevette 8.781e+00 NaN
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## displacement:namechevrolet monte carlo landau -3.639e+01 NaN
## displacement:namechevrolet monte carlo s NA NA
## displacement:namechevrolet monza 2+2 NA NA
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## displacement:namechevrolet nova custom NA NA
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## displacement:namechevrolet vega (sw) NA NA
## displacement:namechevrolet vega 2300 NA NA
## displacement:namechevrolet woody NA NA
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## displacement:namedatsun 200sx NA NA
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## displacement:namedatsun 210 mpg NA NA
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## displacement:namedatsun 510 (sw) NA NA
## displacement:namedatsun 510 hatchback NA NA
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## displacement:namedodge coronet custom (sw) NA NA
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## displacement:nameford galaxie 500 -4.126e+01 NaN
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## displacement:namehonda civic -2.369e+00 NaN
## displacement:namehonda civic (auto) NA NA
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## displacement:namemazda glc NA NA
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## displacement:namemazda glc custom l NA NA
## displacement:namemazda glc deluxe NA NA
## displacement:namemazda rx-4 NA NA
## displacement:namemazda rx-7 gs NA NA
## displacement:namemazda rx2 coupe NA NA
## displacement:namemercedes benz 300d NA NA
## displacement:namemercedes-benz 240d NA NA
## displacement:namemercedes-benz 280s NA NA
## displacement:namemercury capri 2000 NA NA
## displacement:namemercury capri v6 NA NA
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## displacement:namemercury marquis brougham NA NA
## displacement:namemercury monarch NA NA
## displacement:namemercury monarch ghia NA NA
## displacement:namemercury zephyr NA NA
## displacement:namemercury zephyr 6 NA NA
## displacement:namenissan stanza xe NA NA
## displacement:nameoldsmobile cutlass ciera (diesel) NA NA
## displacement:nameoldsmobile cutlass ls NA NA
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## displacement:namepeugeot 304 NA NA
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## displacement:namepeugeot 504 (sw) NA NA
## displacement:namepeugeot 505s turbo diesel NA NA
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## displacement:nameplymouth fury iii -3.956e+01 NaN
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## displacement:nameplymouth horizon 4 NA NA
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## displacement:nameplymouth horizon tc3 NA NA
## displacement:nameplymouth reliant NA NA
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## t value Pr(>|t|)
## (Intercept) NaN NaN
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## displacement:horsepower NaN NaN
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## year:namevw pickup NA NA
## year:namevw rabbit NA NA
## year:namevw rabbit c (diesel) NA NA
## year:namevw rabbit custom NA NA
## origin:nameamc ambassador dpl NA NA
## origin:nameamc ambassador sst NA NA
## origin:nameamc concord NA NA
## origin:nameamc concord d/l NA NA
## origin:nameamc concord dl 6 NA NA
## origin:nameamc gremlin NA NA
## origin:nameamc hornet NA NA
## origin:nameamc hornet sportabout (sw) NA NA
## origin:nameamc matador NA NA
## origin:nameamc matador (sw) NA NA
## origin:nameamc pacer NA NA
## origin:nameamc pacer d/l NA NA
## origin:nameamc rebel sst NA NA
## origin:nameamc spirit dl NA NA
## origin:nameaudi 100 ls NA NA
## origin:nameaudi 100ls NA NA
## origin:nameaudi 4000 NA NA
## origin:nameaudi 5000 NA NA
## origin:nameaudi 5000s (diesel) NA NA
## origin:nameaudi fox NA NA
## origin:namebmw 2002 NA NA
## origin:namebmw 320i NA NA
## origin:namebuick century NA NA
## origin:namebuick century 350 NA NA
## origin:namebuick century limited NA NA
## origin:namebuick century luxus (sw) NA NA
## origin:namebuick century special NA NA
## origin:namebuick electra 225 custom NA NA
## origin:namebuick estate wagon (sw) NA NA
## origin:namebuick lesabre custom NA NA
## origin:namebuick opel isuzu deluxe NA NA
## origin:namebuick regal sport coupe (turbo) NA NA
## origin:namebuick skyhawk NA NA
## origin:namebuick skylark NA NA
## origin:namebuick skylark 320 NA NA
## origin:namebuick skylark limited NA NA
## origin:namecadillac eldorado NA NA
## origin:namecadillac seville NA NA
## origin:namecapri ii NA NA
## origin:namechevroelt chevelle malibu NA NA
## origin:namechevrolet bel air NA NA
## origin:namechevrolet camaro NA NA
## origin:namechevrolet caprice classic NA NA
## origin:namechevrolet cavalier NA NA
## origin:namechevrolet cavalier 2-door NA NA
## origin:namechevrolet cavalier wagon NA NA
## origin:namechevrolet chevelle concours (sw) NA NA
## origin:namechevrolet chevelle malibu NA NA
## origin:namechevrolet chevelle malibu classic NA NA
## origin:namechevrolet chevette NA NA
## origin:namechevrolet citation NA NA
## origin:namechevrolet concours NA NA
## origin:namechevrolet impala NA NA
## origin:namechevrolet malibu NA NA
## origin:namechevrolet malibu classic (sw) NA NA
## origin:namechevrolet monte carlo NA NA
## origin:namechevrolet monte carlo landau NA NA
## origin:namechevrolet monte carlo s NA NA
## origin:namechevrolet monza 2+2 NA NA
## origin:namechevrolet nova NA NA
## origin:namechevrolet nova custom NA NA
## origin:namechevrolet vega NA NA
## origin:namechevrolet vega (sw) NA NA
## origin:namechevrolet vega 2300 NA NA
## origin:namechevrolet woody NA NA
## origin:namechevy c10 NA NA
## origin:namechevy c20 NA NA
## origin:namechevy s-10 NA NA
## origin:namechrysler cordoba NA NA
## origin:namechrysler lebaron medallion NA NA
## origin:namechrysler lebaron salon NA NA
## origin:namechrysler lebaron town @ country (sw) NA NA
## origin:namechrysler new yorker brougham NA NA
## origin:namechrysler newport royal NA NA
## origin:namedatsun 1200 NA NA
## origin:namedatsun 200-sx NA NA
## origin:namedatsun 200sx NA NA
## origin:namedatsun 210 NA NA
## origin:namedatsun 210 mpg NA NA
## origin:namedatsun 280-zx NA NA
## origin:namedatsun 310 NA NA
## origin:namedatsun 310 gx NA NA
## origin:namedatsun 510 NA NA
## origin:namedatsun 510 (sw) NA NA
## origin:namedatsun 510 hatchback NA NA
## origin:namedatsun 610 NA NA
## origin:namedatsun 710 NA NA
## origin:namedatsun 810 NA NA
## origin:namedatsun 810 maxima NA NA
## origin:namedatsun b-210 NA NA
## origin:namedatsun b210 NA NA
## origin:namedatsun b210 gx NA NA
## origin:namedatsun f-10 hatchback NA NA
## origin:namedatsun pl510 NA NA
## origin:namedodge aries se NA NA
## origin:namedodge aries wagon (sw) NA NA
## origin:namedodge aspen NA NA
## origin:namedodge aspen 6 NA NA
## origin:namedodge aspen se NA NA
## origin:namedodge challenger se NA NA
## origin:namedodge charger 2.2 NA NA
## origin:namedodge colt NA NA
## origin:namedodge colt (sw) NA NA
## origin:namedodge colt hardtop NA NA
## origin:namedodge colt hatchback custom NA NA
## origin:namedodge colt m/m NA NA
## origin:namedodge coronet brougham NA NA
## origin:namedodge coronet custom NA NA
## origin:namedodge coronet custom (sw) NA NA
## origin:namedodge d100 NA NA
## origin:namedodge d200 NA NA
## origin:namedodge dart custom NA NA
## origin:namedodge diplomat NA NA
## origin:namedodge magnum xe NA NA
## origin:namedodge monaco (sw) NA NA
## origin:namedodge monaco brougham NA NA
## origin:namedodge omni NA NA
## origin:namedodge rampage NA NA
## origin:namedodge st. regis NA NA
## origin:namefiat 124 sport coupe NA NA
## origin:namefiat 124 tc NA NA
## origin:namefiat 124b NA NA
## origin:namefiat 128 NA NA
## origin:namefiat 131 NA NA
## origin:namefiat strada custom NA NA
## origin:namefiat x1.9 NA NA
## origin:nameford country NA NA
## origin:nameford country squire (sw) NA NA
## origin:nameford escort 2h NA NA
## origin:nameford escort 4w NA NA
## origin:nameford f108 NA NA
## origin:nameford f250 NA NA
## origin:nameford fairmont NA NA
## origin:nameford fairmont (auto) NA NA
## origin:nameford fairmont (man) NA NA
## origin:nameford fairmont 4 NA NA
## origin:nameford fairmont futura NA NA
## origin:nameford fiesta NA NA
## origin:nameford futura NA NA
## origin:nameford galaxie 500 NA NA
## origin:nameford gran torino NA NA
## origin:nameford gran torino (sw) NA NA
## origin:nameford granada NA NA
## origin:nameford granada ghia NA NA
## origin:nameford granada gl NA NA
## origin:nameford granada l NA NA
## origin:nameford ltd NA NA
## origin:nameford ltd landau NA NA
## origin:nameford maverick NA NA
## origin:nameford mustang NA NA
## origin:nameford mustang gl NA NA
## origin:nameford mustang ii NA NA
## origin:nameford mustang ii 2+2 NA NA
## origin:nameford pinto NA NA
## origin:nameford pinto (sw) NA NA
## origin:nameford pinto runabout NA NA
## origin:nameford ranger NA NA
## origin:nameford thunderbird NA NA
## origin:nameford torino NA NA
## origin:nameford torino 500 NA NA
## origin:namehi 1200d NA NA
## origin:namehonda accord NA NA
## origin:namehonda accord cvcc NA NA
## origin:namehonda accord lx NA NA
## origin:namehonda civic NA NA
## origin:namehonda civic (auto) NA NA
## origin:namehonda civic 1300 NA NA
## origin:namehonda civic 1500 gl NA NA
## origin:namehonda civic cvcc NA NA
## origin:namehonda prelude NA NA
## origin:namemaxda glc deluxe NA NA
## origin:namemaxda rx3 NA NA
## origin:namemazda 626 NA NA
## origin:namemazda glc NA NA
## origin:namemazda glc 4 NA NA
## origin:namemazda glc custom NA NA
## origin:namemazda glc custom l NA NA
## origin:namemazda glc deluxe NA NA
## origin:namemazda rx-4 NA NA
## origin:namemazda rx-7 gs NA NA
## origin:namemazda rx2 coupe NA NA
## origin:namemercedes benz 300d NA NA
## origin:namemercedes-benz 240d NA NA
## origin:namemercedes-benz 280s NA NA
## origin:namemercury capri 2000 NA NA
## origin:namemercury capri v6 NA NA
## origin:namemercury cougar brougham NA NA
## origin:namemercury grand marquis NA NA
## origin:namemercury lynx l NA NA
## origin:namemercury marquis NA NA
## origin:namemercury marquis brougham NA NA
## origin:namemercury monarch NA NA
## origin:namemercury monarch ghia NA NA
## origin:namemercury zephyr NA NA
## origin:namemercury zephyr 6 NA NA
## origin:namenissan stanza xe NA NA
## origin:nameoldsmobile cutlass ciera (diesel) NA NA
## origin:nameoldsmobile cutlass ls NA NA
## origin:nameoldsmobile cutlass salon brougham NA NA
## origin:nameoldsmobile cutlass supreme NA NA
## origin:nameoldsmobile delta 88 royale NA NA
## origin:nameoldsmobile omega NA NA
## origin:nameoldsmobile omega brougham NA NA
## origin:nameoldsmobile starfire sx NA NA
## origin:nameoldsmobile vista cruiser NA NA
## origin:nameopel 1900 NA NA
## origin:nameopel manta NA NA
## origin:namepeugeot 304 NA NA
## origin:namepeugeot 504 NA NA
## origin:namepeugeot 504 (sw) NA NA
## origin:namepeugeot 505s turbo diesel NA NA
## origin:namepeugeot 604sl NA NA
## origin:nameplymouth 'cuda 340 NA NA
## origin:nameplymouth arrow gs NA NA
## origin:nameplymouth champ NA NA
## origin:nameplymouth cricket NA NA
## origin:nameplymouth custom suburb NA NA
## origin:nameplymouth duster NA NA
## origin:nameplymouth fury NA NA
## origin:nameplymouth fury gran sedan NA NA
## origin:nameplymouth fury iii NA NA
## origin:nameplymouth grand fury NA NA
## origin:nameplymouth horizon NA NA
## origin:nameplymouth horizon 4 NA NA
## origin:nameplymouth horizon miser NA NA
## origin:nameplymouth horizon tc3 NA NA
## origin:nameplymouth reliant NA NA
## origin:nameplymouth sapporo NA NA
## origin:nameplymouth satellite NA NA
## origin:nameplymouth satellite custom NA NA
## origin:nameplymouth satellite custom (sw) NA NA
## origin:nameplymouth satellite sebring NA NA
## origin:nameplymouth valiant NA NA
## origin:nameplymouth valiant custom NA NA
## origin:nameplymouth volare NA NA
## origin:nameplymouth volare custom NA NA
## origin:nameplymouth volare premier v8 NA NA
## origin:namepontiac astro NA NA
## origin:namepontiac catalina NA NA
## origin:namepontiac catalina brougham NA NA
## origin:namepontiac firebird NA NA
## origin:namepontiac grand prix NA NA
## origin:namepontiac grand prix lj NA NA
## origin:namepontiac j2000 se hatchback NA NA
## origin:namepontiac lemans v6 NA NA
## origin:namepontiac phoenix NA NA
## origin:namepontiac phoenix lj NA NA
## origin:namepontiac safari (sw) NA NA
## origin:namepontiac sunbird coupe NA NA
## origin:namepontiac ventura sj NA NA
## origin:namerenault 12 (sw) NA NA
## origin:namerenault 12tl NA NA
## origin:namerenault 5 gtl NA NA
## origin:namesaab 99e NA NA
## origin:namesaab 99gle NA NA
## origin:namesaab 99le NA NA
## origin:namesubaru NA NA
## origin:namesubaru dl NA NA
## origin:nametoyota carina NA NA
## origin:nametoyota celica gt NA NA
## origin:nametoyota celica gt liftback NA NA
## origin:nametoyota corolla NA NA
## origin:nametoyota corolla 1200 NA NA
## origin:nametoyota corolla 1600 (sw) NA NA
## origin:nametoyota corolla liftback NA NA
## origin:nametoyota corolla tercel NA NA
## origin:nametoyota corona NA NA
## origin:nametoyota corona hardtop NA NA
## origin:nametoyota corona liftback NA NA
## origin:nametoyota corona mark ii NA NA
## origin:nametoyota cressida NA NA
## origin:nametoyota mark ii NA NA
## origin:nametoyota starlet NA NA
## origin:nametoyota tercel NA NA
## origin:nametoyouta corona mark ii (sw) NA NA
## origin:nametriumph tr7 coupe NA NA
## origin:namevokswagen rabbit NA NA
## origin:namevolkswagen 1131 deluxe sedan NA NA
## origin:namevolkswagen 411 (sw) NA NA
## origin:namevolkswagen dasher NA NA
## origin:namevolkswagen jetta NA NA
## origin:namevolkswagen model 111 NA NA
## origin:namevolkswagen rabbit NA NA
## origin:namevolkswagen rabbit custom NA NA
## origin:namevolkswagen rabbit custom diesel NA NA
## origin:namevolkswagen rabbit l NA NA
## origin:namevolkswagen scirocco NA NA
## origin:namevolkswagen super beetle NA NA
## origin:namevolkswagen type 3 NA NA
## origin:namevolvo 144ea NA NA
## origin:namevolvo 145e (sw) NA NA
## origin:namevolvo 244dl NA NA
## origin:namevolvo 245 NA NA
## origin:namevolvo 264gl NA NA
## origin:namevolvo diesel NA NA
## origin:namevw dasher (diesel) NA NA
## origin:namevw pickup NA NA
## origin:namevw rabbit NA NA
## origin:namevw rabbit c (diesel) NA NA
## origin:namevw rabbit custom NA NA
##
## Residual standard error: NaN on 0 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: NaN
## F-statistic: NaN on 391 and 0 DF, p-value: NA- (h)[5 pts] Try a few different transformations of the variables, such as \(\log(X), \sqrt{X}, X^2\). Comment on your findings.
# Fit Linear Regression model with different transformation
different_transformation <- lm(mpg ~ . + I(log(displacement)) + I(sqrt(weight)) + I(weight^2), data = dataAuto)
# Output the summary of the different transformation
summary(different_transformation)##
## Call:
## lm(formula = mpg ~ . + I(log(displacement)) + I(sqrt(weight)) +
## I(weight^2), data = dataAuto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.639 0.000 0.000 0.000 5.639
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.535e+00 1.076e+02 -0.061 0.951706
## cylinders -6.653e-01 6.718e-01 -0.990 0.324909
## displacement 3.514e-02 3.236e-02 1.086 0.280662
## horsepower -2.459e-02 3.396e-02 -0.724 0.471011
## weight -4.243e-02 7.319e-02 -0.580 0.563706
## acceleration -4.877e-01 1.787e-01 -2.729 0.007779
## year 7.294e-01 1.152e-01 6.330 1.23e-08
## origin -2.427e+00 4.332e+00 -0.560 0.576845
## nameamc ambassador dpl 3.297e+00 3.159e+00 1.044 0.299758
## nameamc ambassador sst 3.929e+00 3.186e+00 1.233 0.220970
## nameamc concord 8.841e-02 3.222e+00 0.027 0.978173
## nameamc concord d/l -7.853e-01 3.341e+00 -0.235 0.814763
## nameamc concord dl 6 5.377e-01 3.477e+00 0.155 0.877464
## nameamc gremlin 1.207e+00 3.098e+00 0.389 0.697970
## nameamc hornet 1.747e+00 2.984e+00 0.586 0.559714
## nameamc hornet sportabout (sw) 1.607e+00 3.560e+00 0.451 0.652943
## nameamc matador 1.394e+00 2.617e+00 0.533 0.595810
## nameamc matador (sw) 2.933e+00 2.821e+00 1.040 0.301502
## nameamc pacer 1.481e+00 3.505e+00 0.422 0.673805
## nameamc pacer d/l 2.795e-02 3.522e+00 0.008 0.993687
## nameamc rebel sst 3.883e+00 3.235e+00 1.200 0.233490
## nameamc spirit dl -1.288e+00 4.134e+00 -0.312 0.756073
## nameaudi 100 ls 2.481e+00 3.484e+00 0.712 0.478444
## nameaudi 100ls -1.574e+00 3.072e+00 -0.512 0.609831
## nameaudi 4000 4.205e+00 3.209e+00 1.311 0.193668
## nameaudi 5000 -2.387e+00 3.465e+00 -0.689 0.492735
## nameaudi 5000s (diesel) 1.319e+01 3.731e+00 3.536 0.000672
## nameaudi fox 3.931e+00 3.301e+00 1.191 0.237069
## namebmw 2002 4.340e+00 3.473e+00 1.250 0.214907
## namebmw 320i -3.898e+00 3.336e+00 -1.168 0.246000
## namebuick century 2.580e+00 2.988e+00 0.863 0.390531
## namebuick century 350 1.680e+00 3.179e+00 0.528 0.598662
## namebuick century limited 4.986e-01 3.643e+00 0.137 0.891457
## namebuick century luxus (sw) 1.969e+00 3.447e+00 0.571 0.569464
## namebuick century special 1.244e+00 3.387e+00 0.367 0.714329
## namebuick electra 225 custom 1.329e+00 3.958e+00 0.336 0.737894
## namebuick estate wagon (sw) 1.540e+00 2.873e+00 0.536 0.593412
## namebuick lesabre custom 2.859e+00 3.299e+00 0.867 0.388677
## namebuick opel isuzu deluxe 2.064e-01 4.092e+00 0.050 0.959894
## namebuick regal sport coupe (turbo) -1.135e+00 3.654e+00 -0.311 0.756845
## namebuick skyhawk 2.362e+00 3.435e+00 0.688 0.493649
## namebuick skylark 5.986e-01 3.223e+00 0.186 0.853127
## namebuick skylark 320 3.848e+00 3.160e+00 1.218 0.226736
## namebuick skylark limited 1.979e+00 3.878e+00 0.510 0.611179
## namecadillac eldorado 7.745e+00 3.380e+00 2.292 0.024497
## namecadillac seville 3.200e+00 3.326e+00 0.962 0.338837
## namecapri ii -5.808e-01 3.911e+00 -0.149 0.882302
## namechevroelt chevelle malibu 1.952e+00 3.423e+00 0.570 0.570054
## namechevrolet bel air 2.585e+00 3.263e+00 0.792 0.430598
## namechevrolet camaro 7.029e-02 3.891e+00 0.018 0.985631
## namechevrolet caprice classic 1.155e+00 2.636e+00 0.438 0.662435
## namechevrolet cavalier -1.265e+00 4.197e+00 -0.301 0.763861
## namechevrolet cavalier 2-door 3.192e+00 4.181e+00 0.763 0.447406
## namechevrolet cavalier wagon -2.623e+00 4.207e+00 -0.624 0.534672
## namechevrolet chevelle concours (sw) 1.765e+00 3.271e+00 0.540 0.590943
## namechevrolet chevelle malibu 4.098e+00 3.018e+00 1.358 0.178292
## namechevrolet chevelle malibu classic 2.428e+00 2.894e+00 0.839 0.403869
## namechevrolet chevette -3.855e-01 3.744e+00 -0.103 0.918249
## namechevrolet citation 1.665e-01 3.297e+00 0.050 0.959850
## namechevrolet concours 3.038e-03 3.355e+00 0.001 0.999280
## namechevrolet impala 2.480e+00 2.648e+00 0.937 0.351748
## namechevrolet malibu 6.887e-01 2.854e+00 0.241 0.809942
## namechevrolet malibu classic (sw) 1.698e+00 3.298e+00 0.515 0.608164
## namechevrolet monte carlo 2.502e+00 3.548e+00 0.705 0.482744
## namechevrolet monte carlo landau 1.091e+00 2.763e+00 0.395 0.693919
## namechevrolet monte carlo s 2.903e+00 3.207e+00 0.905 0.368078
## namechevrolet monza 2+2 2.998e+00 3.467e+00 0.865 0.389671
## namechevrolet nova 1.404e+00 2.903e+00 0.484 0.629959
## namechevrolet nova custom 1.148e+00 3.466e+00 0.331 0.741236
## namechevrolet vega -3.168e-01 3.451e+00 -0.092 0.927092
## namechevrolet vega (sw) 9.793e-01 3.938e+00 0.249 0.804205
## namechevrolet vega 2300 5.217e+00 3.969e+00 1.314 0.192364
## namechevrolet woody -2.466e+00 4.167e+00 -0.592 0.555584
## namechevy c10 -1.834e+00 3.206e+00 -0.572 0.568934
## namechevy c20 2.955e+00 3.923e+00 0.753 0.453356
## namechevy s-10 2.380e+00 4.114e+00 0.579 0.564449
## namechrysler cordoba 1.479e+00 3.269e+00 0.452 0.652133
## namechrysler lebaron medallion -3.402e+00 3.985e+00 -0.854 0.395688
## namechrysler lebaron salon -3.861e+00 3.522e+00 -1.096 0.276153
## namechrysler lebaron town @ country (sw) 1.793e+00 3.217e+00 0.557 0.578793
## namechrysler new yorker brougham 2.128e+00 3.582e+00 0.594 0.554140
## namechrysler newport royal 2.925e+00 3.264e+00 0.896 0.372763
## namedatsun 1200 1.080e+01 6.542e+00 1.651 0.102477
## namedatsun 200-sx 7.147e-02 6.511e+00 0.011 0.991269
## namedatsun 200sx 7.672e+00 6.494e+00 1.181 0.240827
## namedatsun 210 8.838e+00 6.153e+00 1.436 0.154671
## namedatsun 210 mpg 8.287e+00 6.311e+00 1.313 0.192811
## namedatsun 280-zx 1.207e+01 6.981e+00 1.729 0.087547
## namedatsun 310 7.975e+00 6.225e+00 1.281 0.203713
## namedatsun 310 gx 7.686e+00 6.218e+00 1.236 0.219928
## namedatsun 510 2.909e+00 6.503e+00 0.447 0.655854
## namedatsun 510 (sw) 7.427e+00 6.571e+00 1.130 0.261642
## namedatsun 510 hatchback 1.174e+01 6.475e+00 1.813 0.073428
## namedatsun 610 1.686e+00 6.610e+00 0.255 0.799280
## namedatsun 710 5.928e+00 6.349e+00 0.934 0.353201
## namedatsun 810 2.988e+00 6.993e+00 0.427 0.670309
## namedatsun 810 maxima 2.924e+00 6.927e+00 0.422 0.674110
## namedatsun b-210 5.927e+00 6.308e+00 0.940 0.350158
## namedatsun b210 6.537e+00 6.395e+00 1.022 0.309689
## namedatsun b210 gx 1.287e+01 6.351e+00 2.027 0.045881
## namedatsun f-10 hatchback 6.481e+00 6.272e+00 1.033 0.304514
## namedatsun pl510 5.691e+00 6.297e+00 0.904 0.368791
## namedodge aries se -1.039e+00 4.023e+00 -0.258 0.796780
## namedodge aries wagon (sw) -2.792e+00 3.952e+00 -0.706 0.481954
## namedodge aspen 3.454e-01 3.012e+00 0.115 0.908988
## namedodge aspen 6 8.636e-01 3.377e+00 0.256 0.798780
## namedodge aspen se 3.672e+00 3.412e+00 1.076 0.285011
## namedodge challenger se 2.740e+00 3.241e+00 0.845 0.400354
## namedodge charger 2.2 3.942e+00 4.131e+00 0.954 0.342849
## namedodge colt -1.000e+00 3.653e+00 -0.274 0.784906
## namedodge colt (sw) 9.806e-01 4.171e+00 0.235 0.814725
## namedodge colt hardtop -1.205e+00 4.119e+00 -0.292 0.770663
## namedodge colt hatchback custom 2.574e+00 4.259e+00 0.604 0.547316
## namedodge colt m/m 3.074e+00 4.175e+00 0.736 0.463671
## namedodge coronet brougham 2.068e+00 3.210e+00 0.644 0.521260
## namedodge coronet custom 2.022e+00 3.159e+00 0.640 0.523782
## namedodge coronet custom (sw) 2.221e+00 3.327e+00 0.668 0.506200
## namedodge d100 -1.496e+00 3.168e+00 -0.472 0.638037
## namedodge d200 3.504e+00 3.942e+00 0.889 0.376634
## namedodge dart custom 1.287e-01 3.221e+00 0.040 0.968219
## namedodge diplomat 2.753e+00 3.201e+00 0.860 0.392270
## namedodge magnum xe 1.974e+00 3.201e+00 0.617 0.539245
## namedodge monaco (sw) 2.443e+00 3.797e+00 0.643 0.521796
## namedodge monaco brougham 9.551e-01 3.199e+00 0.299 0.766063
## namedodge omni -8.939e-02 4.192e+00 -0.021 0.983038
## namedodge rampage -1.000e+00 4.204e+00 -0.238 0.812559
## namedodge st. regis 1.939e+00 3.226e+00 0.601 0.549544
## namefiat 124 sport coupe 1.497e+00 3.330e+00 0.450 0.654113
## namefiat 124 tc 9.420e-01 3.323e+00 0.284 0.777490
## namefiat 124b 4.587e+00 3.318e+00 1.382 0.170589
## namefiat 128 -8.733e-01 2.974e+00 -0.294 0.769782
## namefiat 131 2.616e+00 3.346e+00 0.782 0.436589
## namefiat strada custom 6.459e+00 3.224e+00 2.003 0.048433
## namefiat x1.9 2.780e+00 3.320e+00 0.837 0.404860
## nameford country 1.053e+00 3.652e+00 0.288 0.773878
## nameford country squire (sw) 1.395e+00 2.857e+00 0.488 0.626795
## nameford escort 2h -5.486e-01 4.339e+00 -0.126 0.899706
## nameford escort 4w 6.725e-01 4.246e+00 0.158 0.874542
## nameford f108 -1.228e+00 3.215e+00 -0.382 0.703424
## nameford f250 3.143e+00 3.934e+00 0.799 0.426595
## nameford fairmont 4.750e-01 3.901e+00 0.122 0.903391
## nameford fairmont (auto) -1.718e+00 3.582e+00 -0.480 0.632752
## nameford fairmont (man) -1.244e+00 3.926e+00 -0.317 0.752141
## nameford fairmont 4 -3.211e+00 3.906e+00 -0.822 0.413368
## nameford fairmont futura -4.133e+00 3.971e+00 -1.041 0.301003
## nameford fiesta 3.099e+00 4.277e+00 0.725 0.470785
## nameford futura -1.300e+00 3.370e+00 -0.386 0.700589
## nameford galaxie 500 3.972e+00 2.625e+00 1.513 0.134052
## nameford gran torino 2.167e+00 2.640e+00 0.821 0.414182
## nameford gran torino (sw) 3.360e+00 3.018e+00 1.113 0.268822
## nameford granada 1.992e+00 3.410e+00 0.584 0.560774
## nameford granada ghia 2.858e+00 3.594e+00 0.795 0.428749
## nameford granada gl -2.849e+00 3.554e+00 -0.802 0.425084
## nameford granada l -2.583e+00 3.650e+00 -0.708 0.481156
## nameford ltd 1.711e+00 2.901e+00 0.590 0.556837
## nameford ltd landau -1.928e-02 3.250e+00 -0.006 0.995280
## nameford maverick 1.902e+00 3.113e+00 0.611 0.542912
## nameford mustang 2.114e+00 3.711e+00 0.570 0.570550
## nameford mustang gl -1.951e+00 3.996e+00 -0.488 0.626653
## nameford mustang ii -4.196e+00 3.415e+00 -1.229 0.222666
## nameford mustang ii 2+2 2.360e-01 3.906e+00 0.060 0.951962
## nameford pinto -1.524e+00 3.295e+00 -0.462 0.645082
## nameford pinto (sw) -1.890e+00 3.972e+00 -0.476 0.635395
## nameford pinto runabout -3.224e+00 3.973e+00 -0.812 0.419372
## nameford ranger -1.375e+00 4.099e+00 -0.335 0.738177
## nameford thunderbird 2.304e+00 3.227e+00 0.714 0.477226
## nameford torino 3.952e+00 3.295e+00 1.199 0.233823
## nameford torino 500 4.176e+00 3.667e+00 1.139 0.258134
## namehi 1200d 3.889e+00 4.408e+00 0.882 0.380137
## namehonda accord 6.659e+00 6.176e+00 1.078 0.284079
## namehonda accord cvcc 6.740e+00 6.458e+00 1.044 0.299731
## namehonda accord lx 3.353e+00 6.371e+00 0.526 0.600140
## namehonda civic 5.783e+00 6.112e+00 0.946 0.346900
## namehonda civic (auto) 1.362e+00 6.202e+00 0.220 0.826726
## namehonda civic 1300 3.740e+00 6.191e+00 0.604 0.547419
## namehonda civic 1500 gl 1.421e+01 6.210e+00 2.289 0.024667
## namehonda civic cvcc 7.882e+00 6.210e+00 1.269 0.207956
## namehonda prelude 5.413e+00 6.323e+00 0.856 0.394495
## namemaxda glc deluxe 4.899e+00 6.197e+00 0.791 0.431466
## namemaxda rx3 -9.118e+00 6.293e+00 -1.449 0.151170
## namemazda 626 7.437e+00 6.427e+00 1.157 0.250590
## namemazda glc 1.837e+01 6.311e+00 2.911 0.004633
## namemazda glc 4 4.416e+00 6.224e+00 0.709 0.480058
## namemazda glc custom 1.326e+00 6.272e+00 0.211 0.833038
## namemazda glc custom l 7.770e+00 6.296e+00 1.234 0.220741
## namemazda glc deluxe 5.224e+00 6.348e+00 0.823 0.412944
## namemazda rx-4 -4.742e+00 6.612e+00 -0.717 0.475316
## namemazda rx-7 gs -7.775e+00 6.428e+00 -1.210 0.229942
## namemazda rx2 coupe -6.541e+00 6.520e+00 -1.003 0.318668
## namemercedes benz 300d 7.940e+00 3.915e+00 2.028 0.045820
## namemercedes-benz 240d 9.453e+00 3.797e+00 2.490 0.014799
## namemercedes-benz 280s 1.674e+00 4.010e+00 0.418 0.677372
## namemercury capri 2000 -1.734e+00 4.018e+00 -0.432 0.667226
## namemercury capri v6 -8.350e-01 3.767e+00 -0.222 0.825130
## namemercury cougar brougham 9.286e-01 3.278e+00 0.283 0.777650
## namemercury grand marquis -3.468e-01 3.261e+00 -0.106 0.915557
## namemercury lynx l 2.441e+00 4.277e+00 0.571 0.569785
## namemercury marquis 6.912e-01 3.437e+00 0.201 0.841119
## namemercury marquis brougham 1.135e+00 3.797e+00 0.299 0.765752
## namemercury monarch -1.439e-02 3.701e+00 -0.004 0.996906
## namemercury monarch ghia 2.800e+00 3.227e+00 0.867 0.388202
## namemercury zephyr -2.934e-01 3.543e+00 -0.083 0.934192
## namemercury zephyr 6 -1.585e+00 3.570e+00 -0.444 0.658209
## namenissan stanza xe 8.075e+00 6.453e+00 1.251 0.214398
## nameoldsmobile cutlass ciera (diesel) 1.491e+01 3.751e+00 3.975 0.000151
## nameoldsmobile cutlass ls 9.699e+00 3.690e+00 2.629 0.010231
## nameoldsmobile cutlass salon brougham 5.279e+00 3.164e+00 1.668 0.099105
## nameoldsmobile cutlass supreme 3.691e+00 3.377e+00 1.093 0.277711
## nameoldsmobile delta 88 royale 1.920e+00 3.277e+00 0.586 0.559475
## nameoldsmobile omega -2.300e+00 3.139e+00 -0.733 0.465739
## nameoldsmobile omega brougham 1.741e+00 3.711e+00 0.469 0.640279
## nameoldsmobile starfire sx -5.426e-01 3.834e+00 -0.142 0.887818
## nameoldsmobile vista cruiser 1.253e+00 3.386e+00 0.370 0.712409
## nameopel 1900 2.532e+00 2.948e+00 0.859 0.392768
## nameopel manta 6.845e-02 2.902e+00 0.024 0.981241
## namepeugeot 304 5.960e+00 3.547e+00 1.680 0.096752
## namepeugeot 504 4.235e+00 3.193e+00 1.326 0.188432
## namepeugeot 504 (sw) 3.302e+00 3.798e+00 0.869 0.387178
## namepeugeot 505s turbo diesel 6.159e+00 3.671e+00 1.678 0.097242
## namepeugeot 604sl -1.625e+00 3.845e+00 -0.423 0.673765
## nameplymouth 'cuda 340 7.802e-01 3.245e+00 0.240 0.810604
## nameplymouth arrow gs -2.365e+00 4.033e+00 -0.586 0.559177
## nameplymouth champ 3.796e+00 4.346e+00 0.873 0.384968
## nameplymouth cricket 9.194e-01 4.127e+00 0.223 0.824251
## nameplymouth custom suburb 2.398e+00 3.423e+00 0.701 0.485592
## nameplymouth duster 4.106e+00 3.043e+00 1.349 0.180987
## nameplymouth fury 3.298e+00 3.459e+00 0.953 0.343178
## nameplymouth fury gran sedan 3.078e+00 3.237e+00 0.951 0.344366
## nameplymouth fury iii 3.739e+00 2.615e+00 1.430 0.156500
## nameplymouth grand fury 4.034e+00 3.362e+00 1.200 0.233618
## nameplymouth horizon 1.626e+00 4.266e+00 0.381 0.704015
## nameplymouth horizon 4 1.373e+00 4.274e+00 0.321 0.748793
## nameplymouth horizon miser 3.561e+00 4.274e+00 0.833 0.407232
## nameplymouth horizon tc3 2.596e+00 4.183e+00 0.621 0.536559
## nameplymouth reliant -1.854e+00 3.738e+00 -0.496 0.621192
## nameplymouth sapporo -1.296e+00 3.838e+00 -0.338 0.736410
## nameplymouth satellite 5.440e+00 3.239e+00 1.680 0.096848
## nameplymouth satellite custom 1.703e+00 3.468e+00 0.491 0.624695
## nameplymouth satellite custom (sw) 3.236e+00 3.200e+00 1.011 0.314896
## nameplymouth satellite sebring 2.554e+00 3.422e+00 0.746 0.457540
## nameplymouth valiant 2.407e+00 3.048e+00 0.789 0.432110
## nameplymouth valiant custom 1.190e+00 3.460e+00 0.344 0.731796
## nameplymouth volare 1.774e+00 3.394e+00 0.523 0.602659
## nameplymouth volare custom 1.880e+00 3.403e+00 0.552 0.582239
## nameplymouth volare premier v8 -1.395e+00 3.163e+00 -0.441 0.660382
## namepontiac astro -3.663e-01 3.876e+00 -0.095 0.924942
## namepontiac catalina 3.635e+00 2.747e+00 1.323 0.189384
## namepontiac catalina brougham 3.858e+00 3.262e+00 1.182 0.240437
## namepontiac firebird 4.158e+00 3.536e+00 1.176 0.243088
## namepontiac grand prix 4.482e+00 3.508e+00 1.278 0.205023
## namepontiac grand prix lj 1.007e+00 3.211e+00 0.314 0.754566
## namepontiac j2000 se hatchback -1.078e-01 4.231e+00 -0.025 0.979729
## namepontiac lemans v6 1.002e+00 3.386e+00 0.296 0.768076
## namepontiac phoenix 2.450e+00 3.592e+00 0.682 0.497116
## namepontiac phoenix lj 2.008e+00 3.376e+00 0.595 0.553628
## namepontiac safari (sw) 3.450e+00 4.142e+00 0.833 0.407304
## namepontiac sunbird coupe -2.499e-01 3.854e+00 -0.065 0.948452
## namepontiac ventura sj 2.021e+00 3.372e+00 0.599 0.550576
## namerenault 12 (sw) 2.509e+00 3.413e+00 0.735 0.464266
## namerenault 12tl 7.874e-02 3.222e+00 0.024 0.980562
## namerenault 5 gtl 6.208e+00 3.209e+00 1.934 0.056513
## namesaab 99e 4.645e+00 3.516e+00 1.321 0.190182
## namesaab 99gle -2.263e+00 3.467e+00 -0.653 0.515858
## namesaab 99le 2.059e+00 3.057e+00 0.673 0.502606
## namesubaru 4.358e+00 6.232e+00 0.699 0.486342
## namesubaru dl 5.369e+00 6.171e+00 0.870 0.386794
## nametoyota carina -4.555e-01 6.623e+00 -0.069 0.945335
## nametoyota celica gt 7.041e+00 6.621e+00 1.064 0.290653
## nametoyota celica gt liftback -1.570e+00 6.633e+00 -0.237 0.813453
## nametoyota corolla 5.139e+00 6.086e+00 0.844 0.400852
## nametoyota corolla 1200 7.265e+00 6.225e+00 1.167 0.246513
## nametoyota corolla 1600 (sw) 5.481e+00 6.508e+00 0.842 0.402169
## nametoyota corolla liftback 1.870e+00 6.477e+00 0.289 0.773540
## nametoyota corolla tercel 1.008e+01 6.328e+00 1.593 0.115045
## nametoyota corona 4.273e+00 6.237e+00 0.685 0.495264
## nametoyota corona hardtop 3.958e+00 6.626e+00 0.597 0.551966
## nametoyota corona liftback 6.615e+00 6.644e+00 0.996 0.322371
## nametoyota corona mark ii 5.496e+00 6.688e+00 0.822 0.413544
## nametoyota cressida 4.195e+00 6.968e+00 0.602 0.548796
## nametoyota mark ii 3.376e+00 6.944e+00 0.486 0.628092
## nametoyota starlet 7.850e+00 6.195e+00 1.267 0.208680
## nametoyota tercel 8.495e+00 6.267e+00 1.356 0.178980
## nametoyouta corona mark ii (sw) 3.779e+00 6.684e+00 0.565 0.573394
## nametriumph tr7 coupe 7.689e+00 3.276e+00 2.347 0.021348
## namevokswagen rabbit -2.606e+00 3.148e+00 -0.828 0.410112
## namevolkswagen 1131 deluxe sedan 3.733e+00 3.591e+00 1.040 0.301561
## namevolkswagen 411 (sw) 1.622e+00 3.549e+00 0.457 0.648854
## namevolkswagen dasher -8.623e-01 2.730e+00 -0.316 0.752876
## namevolkswagen jetta 1.949e+00 3.184e+00 0.612 0.542263
## namevolkswagen model 111 3.614e+00 3.477e+00 1.040 0.301590
## namevolkswagen rabbit -2.394e-01 2.770e+00 -0.086 0.931319
## namevolkswagen rabbit custom -2.626e-01 3.169e+00 -0.083 0.934174
## namevolkswagen rabbit custom diesel 1.527e+01 3.366e+00 4.537 1.93e-05
## namevolkswagen rabbit l 4.132e+00 3.231e+00 1.279 0.204605
## namevolkswagen scirocco 9.383e-01 3.140e+00 0.299 0.765823
## namevolkswagen super beetle 2.064e+00 3.474e+00 0.594 0.554169
## namevolkswagen type 3 2.121e+00 3.753e+00 0.565 0.573491
## namevolvo 144ea -1.114e+00 3.593e+00 -0.310 0.757310
## namevolvo 145e (sw) -1.630e+00 3.662e+00 -0.445 0.657432
## namevolvo 244dl -1.179e-01 3.593e+00 -0.033 0.973893
## namevolvo 245 -8.922e-01 3.660e+00 -0.244 0.808044
## namevolvo 264gl -3.031e+00 3.631e+00 -0.835 0.406251
## namevolvo diesel 9.539e+00 3.800e+00 2.510 0.014036
## namevw dasher (diesel) 1.628e+01 3.756e+00 4.335 4.11e-05
## namevw pickup 1.592e+01 3.607e+00 4.413 3.08e-05
## namevw rabbit 5.126e+00 2.725e+00 1.881 0.063486
## namevw rabbit c (diesel) 1.540e+01 3.428e+00 4.492 2.29e-05
## namevw rabbit custom NA NA NA NA
## I(log(displacement)) -1.169e+01 7.640e+00 -1.530 0.129980
## I(sqrt(weight)) 2.719e+00 5.430e+00 0.501 0.617883
## I(weight^2) 2.320e-06 3.810e-06 0.609 0.544305
##
## (Intercept)
## cylinders
## displacement
## horsepower
## weight
## acceleration **
## year ***
## origin
## nameamc ambassador dpl
## nameamc ambassador sst
## nameamc concord
## nameamc concord d/l
## nameamc concord dl 6
## nameamc gremlin
## nameamc hornet
## nameamc hornet sportabout (sw)
## nameamc matador
## nameamc matador (sw)
## nameamc pacer
## nameamc pacer d/l
## nameamc rebel sst
## nameamc spirit dl
## nameaudi 100 ls
## nameaudi 100ls
## nameaudi 4000
## nameaudi 5000
## nameaudi 5000s (diesel) ***
## nameaudi fox
## namebmw 2002
## namebmw 320i
## namebuick century
## namebuick century 350
## namebuick century limited
## namebuick century luxus (sw)
## namebuick century special
## namebuick electra 225 custom
## namebuick estate wagon (sw)
## namebuick lesabre custom
## namebuick opel isuzu deluxe
## namebuick regal sport coupe (turbo)
## namebuick skyhawk
## namebuick skylark
## namebuick skylark 320
## namebuick skylark limited
## namecadillac eldorado *
## namecadillac seville
## namecapri ii
## namechevroelt chevelle malibu
## namechevrolet bel air
## namechevrolet camaro
## namechevrolet caprice classic
## namechevrolet cavalier
## namechevrolet cavalier 2-door
## namechevrolet cavalier wagon
## namechevrolet chevelle concours (sw)
## namechevrolet chevelle malibu
## namechevrolet chevelle malibu classic
## namechevrolet chevette
## namechevrolet citation
## namechevrolet concours
## namechevrolet impala
## namechevrolet malibu
## namechevrolet malibu classic (sw)
## namechevrolet monte carlo
## namechevrolet monte carlo landau
## namechevrolet monte carlo s
## namechevrolet monza 2+2
## namechevrolet nova
## namechevrolet nova custom
## namechevrolet vega
## namechevrolet vega (sw)
## namechevrolet vega 2300
## namechevrolet woody
## namechevy c10
## namechevy c20
## namechevy s-10
## namechrysler cordoba
## namechrysler lebaron medallion
## namechrysler lebaron salon
## namechrysler lebaron town @ country (sw)
## namechrysler new yorker brougham
## namechrysler newport royal
## namedatsun 1200
## namedatsun 200-sx
## namedatsun 200sx
## namedatsun 210
## namedatsun 210 mpg
## namedatsun 280-zx .
## namedatsun 310
## namedatsun 310 gx
## namedatsun 510
## namedatsun 510 (sw)
## namedatsun 510 hatchback .
## namedatsun 610
## namedatsun 710
## namedatsun 810
## namedatsun 810 maxima
## namedatsun b-210
## namedatsun b210
## namedatsun b210 gx *
## namedatsun f-10 hatchback
## namedatsun pl510
## namedodge aries se
## namedodge aries wagon (sw)
## namedodge aspen
## namedodge aspen 6
## namedodge aspen se
## namedodge challenger se
## namedodge charger 2.2
## namedodge colt
## namedodge colt (sw)
## namedodge colt hardtop
## namedodge colt hatchback custom
## namedodge colt m/m
## namedodge coronet brougham
## namedodge coronet custom
## namedodge coronet custom (sw)
## namedodge d100
## namedodge d200
## namedodge dart custom
## namedodge diplomat
## namedodge magnum xe
## namedodge monaco (sw)
## namedodge monaco brougham
## namedodge omni
## namedodge rampage
## namedodge st. regis
## namefiat 124 sport coupe
## namefiat 124 tc
## namefiat 124b
## namefiat 128
## namefiat 131
## namefiat strada custom *
## namefiat x1.9
## nameford country
## nameford country squire (sw)
## nameford escort 2h
## nameford escort 4w
## nameford f108
## nameford f250
## nameford fairmont
## nameford fairmont (auto)
## nameford fairmont (man)
## nameford fairmont 4
## nameford fairmont futura
## nameford fiesta
## nameford futura
## nameford galaxie 500
## nameford gran torino
## nameford gran torino (sw)
## nameford granada
## nameford granada ghia
## nameford granada gl
## nameford granada l
## nameford ltd
## nameford ltd landau
## nameford maverick
## nameford mustang
## nameford mustang gl
## nameford mustang ii
## nameford mustang ii 2+2
## nameford pinto
## nameford pinto (sw)
## nameford pinto runabout
## nameford ranger
## nameford thunderbird
## nameford torino
## nameford torino 500
## namehi 1200d
## namehonda accord
## namehonda accord cvcc
## namehonda accord lx
## namehonda civic
## namehonda civic (auto)
## namehonda civic 1300
## namehonda civic 1500 gl *
## namehonda civic cvcc
## namehonda prelude
## namemaxda glc deluxe
## namemaxda rx3
## namemazda 626
## namemazda glc **
## namemazda glc 4
## namemazda glc custom
## namemazda glc custom l
## namemazda glc deluxe
## namemazda rx-4
## namemazda rx-7 gs
## namemazda rx2 coupe
## namemercedes benz 300d *
## namemercedes-benz 240d *
## namemercedes-benz 280s
## namemercury capri 2000
## namemercury capri v6
## namemercury cougar brougham
## namemercury grand marquis
## namemercury lynx l
## namemercury marquis
## namemercury marquis brougham
## namemercury monarch
## namemercury monarch ghia
## namemercury zephyr
## namemercury zephyr 6
## namenissan stanza xe
## nameoldsmobile cutlass ciera (diesel) ***
## nameoldsmobile cutlass ls *
## nameoldsmobile cutlass salon brougham .
## nameoldsmobile cutlass supreme
## nameoldsmobile delta 88 royale
## nameoldsmobile omega
## nameoldsmobile omega brougham
## nameoldsmobile starfire sx
## nameoldsmobile vista cruiser
## nameopel 1900
## nameopel manta
## namepeugeot 304 .
## namepeugeot 504
## namepeugeot 504 (sw)
## namepeugeot 505s turbo diesel .
## namepeugeot 604sl
## nameplymouth 'cuda 340
## nameplymouth arrow gs
## nameplymouth champ
## nameplymouth cricket
## nameplymouth custom suburb
## nameplymouth duster
## nameplymouth fury
## nameplymouth fury gran sedan
## nameplymouth fury iii
## nameplymouth grand fury
## nameplymouth horizon
## nameplymouth horizon 4
## nameplymouth horizon miser
## nameplymouth horizon tc3
## nameplymouth reliant
## nameplymouth sapporo
## nameplymouth satellite .
## nameplymouth satellite custom
## nameplymouth satellite custom (sw)
## nameplymouth satellite sebring
## nameplymouth valiant
## nameplymouth valiant custom
## nameplymouth volare
## nameplymouth volare custom
## nameplymouth volare premier v8
## namepontiac astro
## namepontiac catalina
## namepontiac catalina brougham
## namepontiac firebird
## namepontiac grand prix
## namepontiac grand prix lj
## namepontiac j2000 se hatchback
## namepontiac lemans v6
## namepontiac phoenix
## namepontiac phoenix lj
## namepontiac safari (sw)
## namepontiac sunbird coupe
## namepontiac ventura sj
## namerenault 12 (sw)
## namerenault 12tl
## namerenault 5 gtl .
## namesaab 99e
## namesaab 99gle
## namesaab 99le
## namesubaru
## namesubaru dl
## nametoyota carina
## nametoyota celica gt
## nametoyota celica gt liftback
## nametoyota corolla
## nametoyota corolla 1200
## nametoyota corolla 1600 (sw)
## nametoyota corolla liftback
## nametoyota corolla tercel
## nametoyota corona
## nametoyota corona hardtop
## nametoyota corona liftback
## nametoyota corona mark ii
## nametoyota cressida
## nametoyota mark ii
## nametoyota starlet
## nametoyota tercel
## nametoyouta corona mark ii (sw)
## nametriumph tr7 coupe *
## namevokswagen rabbit
## namevolkswagen 1131 deluxe sedan
## namevolkswagen 411 (sw)
## namevolkswagen dasher
## namevolkswagen jetta
## namevolkswagen model 111
## namevolkswagen rabbit
## namevolkswagen rabbit custom
## namevolkswagen rabbit custom diesel ***
## namevolkswagen rabbit l
## namevolkswagen scirocco
## namevolkswagen super beetle
## namevolkswagen type 3
## namevolvo 144ea
## namevolvo 145e (sw)
## namevolvo 244dl
## namevolvo 245
## namevolvo 264gl
## namevolvo diesel *
## namevw dasher (diesel) ***
## namevw pickup ***
## namevw rabbit .
## namevw rabbit c (diesel) ***
## namevw rabbit custom
## I(log(displacement))
## I(sqrt(weight))
## I(weight^2)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.206 on 82 degrees of freedom
## Multiple R-squared: 0.9832, Adjusted R-squared: 0.9201
## F-statistic: 15.57 on 309 and 82 DF, p-value: < 2.2e-16